How long

Saw a good buck chasing a doe in the brush right at dusk lastnight. Never gave me a shot. My question is how long will that doe run before giving in and will they stick around the same area come nightfall. Nothing yet this morning

You never know. They could run for miles or stick around.

Never know. It's like the lotto and not scratch offs. Killed one 2 miles away from his summer turf. They travel like lions.

Couple years ago while I was hanging a stand, had a doe run past me with a buck on her tail. Went back the next day and hunted that stand. The same doe came in but this time dragging a bigger buck behind her. Even though the doe walked all around and under my stand, that buck stayed just out of bow range or either not quite in a shooting lane.
I would hunt that spot for at least the next 2 days.

This long

This ^^ You can bet she left a nice scent trail through your area

Some bucks prefer to travel widely in search of doe while others stay close to home. Just depends on the deer and his preferred habits.

The best place to hunt a specific buck is where you last saw him. You might not see him again but at least you are in a spot you know he has been recently.