This interesting answer includes a quote from Space-Track:
From Space-Track.Org FAQ
TLEs can contain future epochs.
About 20 satellites are categorized as "multi-day objects" because their period is so large. Consequently, our data provider propagates the epoch into the future based on perigee to enable better tracking by available sensors when the object finally comes back into view. (emphasis added)
An example is Object 10370 with a 5683.23 minute period.
In my answer I've said:
The epoch could, technically, potentially, be in the past or the future by quite a lot, as long as the satellite isn't falling too quickly, since the SGP4 algorithm propagation is predictable and deterministic.
In other words, the epoch could be next year, as long as when you run a recent, supported SPG4 propagator it produces a fairly accurate answer now. However, most people interpret the epoch as the time of best accuracy, though it doesn't necessarily have to be.
Assuming for the moment that I'm right (always a dangerous assumption) why would "...propagates the epoch into the future based on perigee to enable better tracking by available sensors when the object finally comes back into view." actually be true?
My understanding is that the epoch is just an offset or reference time, and using a well-written SPG4 propagator there is nothing special or particularly accurate in the propagation itself for results close to the epoch time versus far from it, at least mathematically. I am assuming that there is no random number generator, or entropic effect that makes the propagation "fuzzy" or uncertain away from the epoch. If I know a sapcecraft's position at the time $T_1$, I can set the epoch ($T_0$) to last month or last year, and generate a TLE using that epoch that produces the given position when propagating forward to $T_1$.
Is my thinking correct here? Is there really any mathematical basis for the idea that a TLE would be more accurate in the future if the TLE's epoch is chosen to be in the future? I can't see how it would matter, if things are done correctly.
note: peculiarities and caveats related to atmospheric reentry not withstanding.