For Flighty and Flight Aware, yes.
Flighty has several import/sync options, but once they're in it should track changes, etc.
Flight Aware you can manually input/search for a flight (and I think import as well) and once it's there, it stays until you finish the flight (AFAIK).

So you don't need to keep re-entering stuff every time you check the app.
The only times I'm aware of that you will need to re-enter is if the flight changes actually change the flight #. (ie: AA "cancels" your flight and rebooks you on an entirely new itinerary with new flight #'s)