That depends entirely on how much you loosen it. If you loosen it enough the frog will come off. That's how you change the bow hair.

DeeLight41 said

Is it normal for my frog to go loose when I loosen the screw on my bow? I don't remember noticing this before.
When I tighten the screw to play, the frog is stable.

I assume you mean that the edge of the frog is not staying snug against the stick and parallel to it. I expect that when you tighten the hair, there is a gap between the frog and the stick, and when the hair is lax, the frog can wobble against the stick.

If you completely remove the screw and remove the frog, you will see that, when the bow is assembled, the threads of the screw pass through the head of a second screw. That second screw goes into the wood of the frog. Tightening that second screw will bring the frog closer to the stick and stop its wobbling. Try turning that second screw in a half turn at a time until the frog comes pretty snug against the stick.