Excellent question.

Its a matter of preference. Some guys have told me they want that quiver attached to the bow at all times in case they need a follow-up shot.

I play the odds, which means that I know I'll almost never get the chance for a follow-up shot anyway...so I remove the quiver from the bow and hang it nearby on the tree stand or the tree itself.

If you're going to leave it on your bow make sure you practice shooting with it on your bow...and vice-versa.