You have a BookMate, I think.  I've gone through my share of these over the last few years and threw them away when they disintegrated.  That is, until I realized I could reinforce the clear plastic vinyl before I started using it.  Now the plastic on the inside has worn through and it's rubbing the spine of my book where the metal bends and I need to put a small piece of plastic in between (I used one of those jar opener rubber grip things).   I don't close mine anymore, just leave the book open to the last page I've read and it seems to keep the wear and tear to a minimum.

But, I'm pretty sure the material inside that allows you to flatten and bend the spine is similar to those old 'wrist slapper' bracelets the kids were playing with a number of years back.  They were aluminum, I think.  There was some controversy about them, since you could cut yourself on the edges.  They were straight, like a ruler, until you slapped them against your wrist and then they'd curl up around your arm.  I thought about fixing/making these bookcovers myself too, but if that material is metal as you suspect and you can find it, then you'll need to insulate it from the fabric, so it doesn't wear down the edges where it rubs.  You can probably use a couple pieces of heavy cardboard for the two sides and fix the metal band at the center and then cover the whole thing with some type of thin foam/batting and then cover that with the fabric you've chosen.

Try doing a google search and you should find sources for the bands.  I did a quick look and found several.  Good Luck!