I am the only person who has a manga book on my Wishlist.  The same person has now posted this book twice.  Both times it went to me as I'm the only wisher and both times the request has time out.  I've PM'd the poster asking what the problem is that they keep posting the book but aren't sending it and have gotten no reply.  What can I do?  

If it were me I would send a little note to the powers that are PBS. Maybe they can light  a fire under the member. :)

Unfortunately, I don't think there is anything you can do. You can't make them actually mail the book out...

Well then their account should be suspended or closed.  When we joined the club we agreed to send books that are requested, unless there is an RC we cannot fulfill. If they do not want to send the books then they should take  them off their bookshelf or put their account on hold.

Please report them to PBS so the TPTB can take appropriate action.

She may be a new member. I had the same problem with someone repeatedly posting a book and letting it time out.  I PM'ed her and she said that she didn't understand what was going on. The book kept disappearing from her page.  She did not know there was a 5 day time limit for accepting a request. She finally mailed me the book and I had to mark it received from the transaction archive because she didn't mark it mailed before it timed out. Argh!

If they post it a third time without responding to you, send in Feedback. Your PM should prompt them to stop doing it (and answer you). 

More importantly, if he/she keeps posting, another copy might get posted and not go to you as you are tied up waiting on the first poster.

Both times it went to me as I'm the only wisher and both times the request has time out.  I've PM'd the poster asking what the problem is that they keep posting the book but aren't sending it and have gotten no reply.  What can I do?  

 Sounds like they don't know what they are doing and they are possibly new.  I agree, use the contact us link to send a message to PBS.   They can find out what's going on and talk to them and give you feedback.  

I'm wondering if they're a new member, they post the book, it automatically goes to you. However, they don't know to check the "Books Requested From Me" tab, and thus the book times out. Later, they see it's not on their shelf, so they repost. And it goes back to you. Lather, rinse, repeat. Perhaps, assuming they are new, TPTB can ask their Tour Guide to help them out.

They weren't new to PBS.  Now their account says the account is supended or closed.  Guess I won't ever get this book!