I've been saying this for years---control theory analogies
I've thought for years(without understanding the deep physics of it all), why not use control theory as an analog for time streams. In that event you could have stable loops of time. You could also have oscillators, or chaotic fluctuators. To me there is no logical barrier to having such systems. If you get into the parallel universe theory where there is a new universe for every quantum event, then you could go "backwards", but it would be yet another universe anyway (that only seemed like the past). The old Shakespearean, There are more things in heaven and Earth, Horatio, Than are dreamt of in your philosophy," I think continues to apply to all these theories.