The Storm Thrower “Sky Rumbler” attack type says “on a direct hit, the model hit and models within 5in lose flight for one round.”
Can a model gain/regain flight afterwards? Lets say an Eidolon with the flight head gets hit. Can i then put Arcane Propulsion on it to have it gain flight again?
Or similarly, if arcane propulsion is on a jack. It gets hit, loses flight. Can I drop arcane propulsion and recast it to reapply Flight.
That should work, yes. In general, the rules only do what they say they do, and nothing more. 
So, the model hit loses Flight for one round, nice and simple.
The spell or effect would need to say “loses and cannot gain” (or something to that effect) in order to prevent the model from regaining Flight (or the effect in question).
(Caveat: it’s possible that something was added to the core rules yesterday that governs this and I haven’t seen it yet. However, nothing of that sort was added to the change log, so I doubt that it happened.)