JKR: Can't get him out.
ES: He's Dumbledore, he can do anything!
JKR: No, no no no no. Peeves is like dry rot. You can try and eradicate it. It comes with the building. You're stuck. If you've got Peeves you're stuck.
ES: But Peeves answers to Dumbledore
JKR: Allegedly.
MA: Allegedly?
JKR: Yeah. I see Peeves as like a severe plumbing problem in a very old building, and Dumbledore is slightly better with the spanner than most people, so he can maybe make it function better for a few weeks. Then it's going to start leaking again. Would you want Peeves gone, honestly?