IF you ask a follower to leave your group, and they disappear from where you left them, can you ever get them back?
Also,how does charisma and persuade effect the time a follower will wait for you?

I don't know for sure, but I *think* they return to their original place.
Here's a thread about it; you can see there that Sogg, for example, returns to the tavern, while Virgil is trickier to get back.
If you have Apprentice Persuasion skill, they will wait for you longer, and if you have 20+ CH, they won't ever leave your group on their own.

(Just to clarify: Virgil will leave at one point even if you do have CHA >/= 20, as part of his storyline---but he's retrievable. There are also a couple of people you meet along the way who may join your group briefly for a specific task, but then leave---they're not on Prator's list in this forum.)

Indeed, but skwarde only asked about "normal" followers, and he/she is a relatively new player, so Virgil will stay in the party for some more time; that's why I only answered the original question.
A bit of clarification never hurts, of course, so you did well to post.

I figured Sogg would go back to his original tavern in Shrouded Hills, but he wasn't there. I'll have to check the taverns in Tarant

I think my husband found him again by the bridge out of Shrouded Hills when he dropped him. (I never used Sogg myself, so never dropped him anywhere.)

Sogg went to the riverside by Shrouded hills, but since he was there, Virgil never appeared there when I tested booting him from the group.