In an ideal world for you as a player, your character has lots of dramatic things going on at any given time. Stuff is happening, alliances are being forged and broken, betrayals are taking place, and so forth. It's all very entertaining to watch and play. And at various times the characters you're playing will be entirely all right with that, but that's entirely because they think something else is going on that's worth all of the horrible drama.
Be honest -- you probably do not want that level of drama in your daily life. The stuff that your roleplaying characters are subjected to would make you miserable because it's so far over the top that it redefines the entire concept of the top. It's horrible. Your characters tolerate it; most of them don't actively seek it out.
This is the classic problem of writing slasher films. The entire structure of the film relies on people having to deal with circumstances they'd prefer to simply avoid, since in this case "circumstances" is synonymous with "maniac with a murder weapon." As an audience member, you want to see the whole scenario play out; you don't want the protagonists to do the smart thing and just hop in the car after making a quick phone call to the police.
This is why every single film has to explain why characters get locked into the situation. That's a lesson that can be applied to your own characters when you need to keep them somewhere.
If your character doesn't want to stay around and doesn't need to, the first option is making sure that she can't leave. Remove any escape routes. Perhaps she didn't think she needed to stay with this group because she didn't need the money... but money can evaporate, other jobs can go away, and suddenly she does need the money. Or maybe leaving would have more severe consequences, perhaps hurting her seriously in other projects by breaking off ties.
This might be the most toxic group in the world; it could be that your character's guild is the one thing keeping her efforts to ingratiate herself with Stormwind's elite social circle afloat. Or it could be that her fleet in Star Trek Online is what keeps her from facing a court-martial or two.
The obvious objection is that this is just a patch job, and once that problem is fixed, your character is still going to want to leave. But the key is making that take longer. It's possible that by the time that obstacle is overcome, things will have changed enough that your character no longer has the overwhelming desire to leave.
But maybe you can't throw up those roadblocks. Your next option is to give her a motivation for sticking around that overrides her urge to get away from the group. Spite, for instance, serves as a wonderful motivator. You might not like the people, or you might want their drama out of your life, but seeing an opportunity to get back at them can give a lot of people pause about jumping ship.
It's also possible for you to get an external motivation that makes the group more attractive despite the drama. Imagine your character in Guild Wars 2 has a deep need for Canthan relics, and someone he'd just as soon avoid talking to ever again suddenly gets his hands on a lot of relics. Even with all of the drama, your character has good reason to put the distaste to one side and focus on getting those relics for himself.
This is also a good point to talk with people OOC about the situation, since you don't want to come across as if you don't like anyone involved. And presumably, they want you to stick around as well.
But let's say neither of these solutions works. Your character wants to leave, and she can, and there's no compelling reason for her to stay around despite that fact. But you, the player, still want her in place. So what do you to to keep her around?
You give her an even bigger problem.
This isn't the same as giving her a reason to need the group to avoid penalties. This is creating something big enough that even though she could leave the group, she'd still need to find other people to help her deal with the issue, and as badly as she would like better allies, these people are already here. Once the problem is gone, she can leave, but until then she's going to work with these jerks because that's the fastest way to deal with the problem.
This is, admittedly, a kludge. It's meant to give you a reason to work with people for long enough that you can get a better reason moving, and when done too often it feels contrived. But when you want to keep your group together and you have no alternatives, there are worse plots to try.
Feedback is welcome as always in the comments below or via mail to firstname.lastname@example.org. Next week, I'll say bad things about /random. The week after that, we'll talk about the ways people ruin their own RP events.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did. If you need a refresher, check out the Storyboard Library.