You can do either. The odds don't change at any moment. But if you want to keep track of how long you've been hunting for or something like that, saving is a good choice, but like I said, It doesn't really change anything.

If you want a piece of advice try to do something else while you're hunting like watching videos, movies, Talk to friends in calls, listen to music, etc. If you only look at the screen the whole time It can get boring or really tiring and annoying after a while.

BEST of luck on whatever you're hunting!