Age for Change..

[Apokryltaros]

Even computer programs wear out eventually.

I'm not sure what you're talking about there. Computer hardware can wear out. But computer programs themselves don't. Usually a program gets removed from service because the task it does changes.

Sometimes they become damaged, too.

[Lupin]

But active damage/corruption isn't the same thing as wearing out. It isn't like "If I run mspaint.exe 'n' times, when I run it n+1 times it isn't going to work."

[Jamie]

Even computer programs wear out eventually.

I'm not sure what you're talking about there. Computer hardware can wear out. But computer programs themselves don't. Usually a program gets removed from service because the task it does changes.

I mean that the storage media they are on will wear out eventually, and even if they are copied from place to place, tiny errors can slowly creep in that, in theory, over the course of centuries would eventually age them. Kind of like records, tapes, photographs and old movies wear out as more copies are made, get cleaned up and converted to digital to store them "forever", but we are still talking about inevitable degradation that will happen each century. A tiny error here, a tiny error there. Even our attempts to clean these errors up will, in theory, result in more errors.
The ultimate life of a movie, a computer program or any other kind of digital file is probably not more than three thousand years. It might still be watchable, but only to die-hard fans who didn't mind the errors.
I mentioned computer programs as an example because I visualize shapeshifting technology as being like in the "Four Lords of the Diamonds" series by Jack Chalker, where the transformation process is so super-complex that you need what amounts to a computer program in order to run it.
In theory, shapeshifting technology introduced to the human body would itself eventually wear out, even in the best of circumstances. The results might go in tandem with aging, or might resemble aging. Or you might just have an exploding werewolf.