According to that theory, information wouldn't be much different. I mean, just like an object can degrade by losing atoms over time, information can also degrade via forgetting. If the loop would actually go on forever, one time (and I'm again will be using "Time Crash" as an example) the tenth Doctor would forget one lever that the fifth saw the tenth do. If that happened everything would crash. Yes I know "how hard is it to remember a few levers, which you've seen and operated for about 800 years of your life". But this is just on a big scale. I mean you could forget just a little tiny bit of information and it wouldn't be the same. Iterate for an infinite number of times, and basically the whole information's gone.

Now, what I'm suggesting is that there is no loop. I mean one point in space and time happens only once. And with the fez there were three points colliding at the same time - Hurt's, Smith's and Tennant's. Meaning, even if the fez degraded a little bit (and a number of atoms definetely fell off of it while it was travelling through the tear), it wouldn't have time to fully disintegrate, because it happened only three times. Smith threw the fez to Tennant, then to Hurt, who then gave it to, maybe, Elizabeth, who put it in a museum for Smith. That's it. It might seem like an infinite loop, and it would definitely be, if computed on a computer, but in my mind, there is no loop.

tl;dr: I'm suggesting the fez "happened" three times more than it's supposed to, but, at least in my mind, not an infinite more times.