Sorry to say but, to fight Pete continuously, you must commit suicide either by the elevator in his arena or by your own means. I suggest the elevator as activating it guarantees that he will not glitch up.
I think he is one of the bosses that you can fight only once a day, pretty sure this is the case.
You can fight him unlimited times. Only once a day, if you're not connected to xbl.
Also, you don't lose Anarchy stacks when crushing yourself with the elevator. So go on live and and crush yourself all you want to farm Pete.
I did a Pete run just now to verify. It's one of those instant deaths (no switch to third person camera) and Gaige keeps her stacks when that happens. Like when Terra flings her off the map (also an insta-death) I noticed she kept Anarchy stacks. --- . I said runt.