Do thermal cutoff fuses wear out if used below rated temperature?
Yes they do, as you have observed.  When heated significantly, but still below melting point, metal crystal structures tend to rearrange into larger crystals and ultimately the electrical path will degrade- have a look at an old car headlamp bulb.  Premature ageing can result from soldering but even in normal use these devices do degrade.
Perhaps consider a self-resetting PTC fuse if that’s an option.