It’s not just that he has to keep moving – though that’s true, too – but that he can’t stop. That’s can’t, the way you can’t make eggs out of omelets. He’s gotten sick a couple of times, deadly sick, and gone out of his head with fever, and he always comes out of it someplace other than he went into it. He’s been arrested thousands of times and he’s always gone by the second night, poof. The Catholics were especially cranky about it. He felt kind of bad about it the first couple of times – especially when they hauled him back and Longinus was hanging there in a pet – but eventually the novelty wore off and they were just a nuisance. He walked out on them, walked straight out of their tribunal without saying anything, and headed south for a while. He wanted to be alone, so he went and wandered around in the middle of the desert for a decade or two.
One morning he comes trudging out of the dunes and realizes he’s closer to civilization than he’s been in years. Cities look alien enough that he starts down toward whatever one it is, someplace in Morocco, thinking maybe he can get something to eat. He’s sick of cactus.
Longinus is sitting against the wall of the city when he comes up to it, his beaky nose perched over a mustache that’s seen better days, and he’s glowering. “Oh, Christ,” the ex-Roman growls. “You again.”
Ahasuerus blows him a kiss, which just shows that neither of them have learned anything much.
Diana Wynne Jones wrote something a bit similar – 'The Homeward Bounders', where the characters who learn some big secret about how the worlds are run have to wander between them all the time, and they never stay in one place for longer than a month before the boundary starts calling them. Coincidence? Eh?