retired dentist here:
if it's the last tooth in the arch, and you don't want to pay money to maintain it, you'll be fine without it, but I wouldn't just leave an unrestored tooth back there to cause problems. If you aren't going to restore it, you should have it extracted.
Some important factors to consider though:
Does it have a root canal? This minimizes some of the problems you might have, but not all, and if not restored, you should have it extracted.
Why is the crown coming off? is there adequate tooth structure left to retain a new restorative effort? Does your dentist feel confident that there is adequate structure, and confident in the health of the tooth?
Sometimes we "reach", and restore a tooth with questionable long term chances. Sometimes it works, sometimes it doesn't. It's not bad dentistry if it doesn't, as long as the patient has been advised of the existence of less than great outcomes.
What does the rest of that quadrant look like? Do you have a lot of healthy strong teeth to do a tad more of the work than they would have to do if that tooth were strong and functional?
These are things you might want to discuss with your dentist before deciding upon a course of action.
Good Luck