You seem to be confusing how non-lethal damage works—which is totally reasonable, because you’re treating it like it works like lethal damage, which would make sense, but it actually doesn’t.
Non-lethal damage does not affect your hp.1 So it can never make anyone “go to 0 hp.” Instead, you track how much non-lethal damage you’ve taken, as a separate, increasing number, and you check \$d_\text{nonlethal} > hp\$: if that’s true, you are unconscious. The number “0” doesn’t play any special role here.
And since you haven’t taken any lethal damage, your hp is not 0, so your wild shape is not affected. Actually, even if you had taken lethal damage, and your hp was zero, your wild shape still wouldn’t be affected—that only happens when you actually die (at which point you revert to your regular form, but since you’re dead this isn’t all that meaningful for you).2
Which means you keep on regenerating, because you’re still in a form that regenerates. You actually can’t stop, on account of being unconscious and therefore unable to choose to end your wild shape.
The nonlethal damage rules say
When you take nonlethal damage, keep a running total of how much you’ve accumulated. Do not deduct the nonlethal damage number from your current hit points. It is not “real” damage. Instead, when your nonlethal damage equals your current hit points, you’re staggered, and when it exceeds your current hit points, you fall unconscious.
(Emphasis original)
Wild shape says “This ability functions like the alternate form special ability, except as noted here,” and alternate form says “A creature using alternate form reverts to its natural form when killed,” so that’s where that comes from.