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This is a "Wild Mass Guess" entry, where we pull out all the sanity stops on theorizing. The regular entry on this topic is elsewhere. Please see this programme note.
Temporal Paradox
Object loops are not infinite due to The Multiverse.
You do not actually travel in your own timeframe, you simply go to the next timeframe over while alternate you comes to yours. Say, for instance, you take object X from your desk and place it on your desk yesterday, then really you're just shifting the object X over one Multiverse each "loop". Many, many multiverses over, entropy will kick in and object X will degrade and the corresponding you will decide object X looks shoddy and worn out and you'll decide to take object Y instead. Yes, there's going to be an origination and an end point, but so many universes are in between that the chances of our hero being in either one of those two universes is slim.

So while a character in fiction my create what appears to be a stable time loop, it is merely a part of a long progression of loops connecting parallel universes. The object has ceased to move down the timeline vertically with everything else, it's moving horizontally. Eventually the object will degrade and things will be done differently but not in the universe covered by this specific story you are reading/watching/whatever.
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