So I have some experience here. Up until about a year ago I wouldn't have said this, but now I can assure you that EVERYONE CAN BE BROKEN. That is, assuming that your tickler knows what he/she is doing.
I've always been mostly a ler and didn't think of myself as very ticklish. A few spots here and there, a few laughs, but I always felt well in control and never really "worried." For me, it was always fun to watch the tickler try to get the best of me, but alas, never to any avail. What I now realize is that the people tickling me (girlfriends mostly, who were not really tickling "experts") didn't really know how.
That is, until the day I got completely broken down. I'll save the full story for a post of its own, but the gist is this: a female friend of mine who I had known for a while and who was visiting town stayed over. One thing led to another (yada yada yada), and I agreed to let her tie me up.
It started with the usual "haha, that tickles a little" but then quickly turned to "haha, wait wtf, what is happening..." then to "NO WAIT, STOPPPP THIS IS ISN"T..." and finally, I was just screaming incoherently, completely at her mercy. She could tell that I was at a breaking point, and stopped torturing me. After I finally caught my breath, there was a just an awkward silence where I was dumbfounded, embarrassed, and not sure what had just happened, while she just had a big grin on her face.
Bottom line: I still don't think of myself as that ticklish in most circumstances... but it's still possible to be broken given the right person.