No, the Defiant would not degrade. It's not trapped in a loop.
After the ship is transported to the Mirror Universe (and back in time), pretty much anything can happen to it after that. It's not like the ship has to survive into the 23rd century in order to be sent back in time again, because it's a different version of the ship that gets sent back.
Think of it this way:
- Sometime in the 23rd century, the Defiant is constructed.
- The ship is commissioned and begins its normal Starfleet service record (mentioned by Saru in a throwaway line in "Despite Yourself")
- Shortly before the events of "The Tholian Web", the Defiant becomes trapped in interphasic space.
- Sometime AFTER that episode, it disappears and ends up in the 22nd century of the Mirror Universe.
- Whatever happens to the Defiant after that, is pretty much irrelevant, because the ORIGINAL Defiant will one day be built in the regular universe's 23rd century.
The thrust of the gist is, the "old" ship doesn't have to survive long enough to become its own original counterpart, because a brand new Defiant will one day be built - that's what always happens. There is a loop, yes, but it's not the same ship that gets used over and over again. The Defiant is built, gets sent back in time, probably serves for awhile in the MU, is destroyed and never seen again, and (decades later, in the Regular Universe) its original "self" is built which will later have all those things happen to it, etc. etc.
To rephrase: If you travel back in time - far enough back so that you arrive before you are born - obviously you don't become your own younger self. Your "old self" may die, but your younger self is destined to be born, because that's what history records. Same goes for the Defiant.