As you might guess, the question in the title is not purely theoretical.

On 11/20/2014, I clicked on the appropriate button to say that I had just mailed a book which someone had ordered from me on PBS. I used prepaid postage with a tracking number barcode, so I'm able to follow the path the book took over the next couple of days.

According to the info that comes up when I click on "Details," USPS marked it as "Delivered - Memphis TN" just two days after I'd posted it. That was mid-afternoon on 11/22/2014.

The person who ordered that book has not yet clicked to acknowledge that it arrived safe and sound. (Nor has he registered any complaints about what sort of condition it was in when the mail carrier delivered it.) 

At first, the delay was no big deal to me. Thanksgiving was coming up, and it was quite possible that the guy was out of town visiting relatives or something, and would go through a ton of accumulated mail and then click to acknowledge receipt whenever he came back. Since I'd already received 1 credit for that book when I first marked it as "mailed," I wasn't holding my breath waiting for the guy to formally acknowledge delivery. But now it's been 23 days since I mailed the silly thing, and I'm wondering what PBS will do when the 26-day mark comes around.

(A few months ago, a two-book PBS package addressed to me failed to materialize in my mailbox. After 26 days, I got an automated message saying my 2 credits were being transferred back to my account. Thus far, that's the one and only time that's happened to me, from either end of the transaction -- a package getting lost in the mail.) 

I'm basically asking for advice on the etiquette here: Should I send the recipient a PM asking what happened? Should I leave it to PBS to send him reminders? (I seem to recall that I got some during my own long wait for that parcel that never arrived at my end.) What will PBS do, given that the online data clearly says the USPS records it as "delivered," if the 26-day deadline rolls around and the guy still has not clicked to say it was, in fact, received? Have any of you been through something similar?

As to what will happen, the receiver will get his credit back from PBS when the book officially goes lost in the mail.

If you purchased postage from PBS, which it seems you did, then you will also keep the credit that you got when you marked the book mailed. That's part of the credit assurance that you pay to PBS when you purchase postage thru them. The extra credit comes out of PBS's pocket.

As to the etiquette, it's fine to PM the other member and politely ask them if they received the package. I usually wait until just before the book goes lst to send a PM like that. Just keep in mind that even though the book has a delivery scan, that just means that the book was delivered somewhere ... not necessarily to the right address. It's not uncommon for books to be misdelivered occasionally.

I oncen saw  that a book was scanned as delivered to me, and it didn't actually appear in my mailbox for 16 more days ... so sometimes the post office messes up.

As to this happening to other people .... sure, it happens, but it's not all that common. I've personally mailed more than 1600 books, and I've only had 2 that  were never marked received eventually. 

As Sara already suggested, I would wait until near the 26-day lost-in-the-mail time frame and politely PM the requestor to ask if the book was received. Since it's already been 23 days, the time to do that would be in the next day or two at latest if you want a response before the book goes lost in the mail

Things happen, such as the requestor being away from home or having more important life situations to deal with, or perhaps the Post Office could have messed up, for example.

I suggest reading the Help Center docs for If a book you sent hasn't been marked received yet... and A book I sent is lost in the mail!

ETA: Links to Help Center docs can be tricky to get right, hence the multiple edits. :-)

PBS will send the other member reminder emails. For normal lost books, two reminders are sent. As this one is reported as delivered, a different worded reminder is sent. You will keep your credit no matter what happens.

At the point of 26 days, the book order will be moved to your Transaction Archive.

Their credit should be returned to them when the book is marked as lost, with some strings. If they have other books that this happens to, then their account will become flagged to be reviewed. Their last log in checked. They may be put on Hold while PBS tries to contact them.

If a member receives a book after it was marked lost in the mail it can be marked "received" from the transaction archive. If this happens and the requestor doesn't know what to do you can refer him to the Help Center doc for I received a book that was 'lost in the mail'

If you are not able to send the link to the requestor, then you can suggest entering "I received a book that was 'lost in the mail' " as a Help Center search term.

If I used PBS postage on a package, I'd wait a few days after the "delivered" scan, then send a PM saying that it was scanned as delivered, and that I hope it had arrived.  I'd ask the member to please let me know if it hadn't arrived.  If I hadn't heard back in 5 days to a week, I'd send in feedback.

If I hadn't used PBS postage or PBS delivery confirmation, I would still send a PM a few days after it was scanned as delivered.  (I don't wait too long, because if people have a lot of books coming in, they may have trouble remembering mine, if too much time has passed.)  I would wait until the system marked the book "lost" before sending in Feedback. 
 

It is possible that the book was delivered to the requestor's house, but that she is on vacation or something and hasn't seen it yet.

That said, a short PM asking, "Did it arrive?" is not unreasonable.  (I've done this with my brother when I've sent him a package that he hasn't acknowledged, and often it's gotten lost in a stack of mail on the kitchen counter!)

In my experience, this is the time of the year that members are more likely to neglect to mark a book received. A PM is perfectly acceptable to politely ask if it has been received and I also include instructions on how to mark a book received from the transaction archive after it has been declared lost. If you do not receive a response within a week, definitely let PBS know that that member is not responding and they will look at the account and perhaps mark it received. Having said that, you have your credit already from using PBS tracking...
 

As everyone else said above, I would send a friendly note checking in. Once I did so and the recipient discovered her apartment complex was holding it hostage (another thing that's more likely to happen this time of year). 

Once I sent a note and the person found the package behind their mail table, it had fallen off the table before they opened it.

I've only had 2 books ever go lost en-route to me.  One showed a delivery scan but it was not delivered to my house and none of my neighbors admitted to having received it by mistake.  So it's possible that the book was miss-delivered. I would send a PM and ask them about it.

Looks like you use PBS postage and have your credit already.  If PBS every reviews your account they can see that the book was scanned delivered if it ends up as a lost book on your account.  They are already sending reminders to the other member.  PBS can also see if this person has a high # of losses or looks like they have gone inactive.

Once I received a note and the book had been delivered to a door we never use.  So absolutely, send a nice note.  I usually send it 7 to 10 days as scan says delivered.  As a matter of fact I'm getting ready to send one as we speak. 

Yes you should PM. The Help Center on the situation asks that you contact the member a few days after the book has been marked delivered. If they never mark the book received, the system has no alternative but to assume the requester did not get the book and will not mark it received, but return the credit. Contacting members and inquiring reduces the number of books not marked because they were overlooked, misplaced, or misdelivered and that in turn cuts down on the number of books marked lost and credits returned by the Credit Assurance system, which will help keep that service available and the cost low.

If a book you sent hasn't been marked received yet... 

I usually wait for PBS to notify me that the book has gone lost.  Then I PM the requester and say I'm sorry the book went lost, and if/when it is received I would appreciate that it be marked appropriately.

Conversely, when someone sends me a book and it is marked lost by PBS I send a PM to the sender, indicating that I did not receive the book, but if/when it is received, I will mark it appropriately.  Good luck. Pat

I also agree, send a polite message.  As this has the potential to be a 'problem' swap, receiving member is highly encouraged to reply.  There are various potential scenarios, but basically if nobody knows there's a problem nobody is looking for a solution (such as the member looking around their mail area or the PO checking with route drivers).