This might be a dumb question, but how far out are really accurate predictions of satellite locations good for without measurement? Like, if I kept scrolling forwards in time, how long would it take before the prediction of the satellite's location was off by an arcsecond (I'm guessing days)? Or a full degree (I'm guessing many years)?
For something in LEO, an arcsecond of error is only a few meters. If you're plugging data into a standard orbital model like SDP4, a few meters is within the typical error margin basically as soon as the TLEs are published.
A full degree of error would take a while. For what it's worth, NORAD publishes new TLEs for things in LEO pretty regularly, sometimes multiple times a day. For higher up objects it can be more than a week before the refresh the data.
ISS elevation chart where you can clearly see when they boosted up: https://www.heavens-above.com/IssHeight.aspx