JBB, the issue is almost certainly your knot. I am assuming you are using a typical float fishing set up of float on mailline, weight above swivel, then leader off the swivel to your hook/lure? If your mainline were breaking then it could be a chipped eyelet on your rod that is chaffing the line. But using this set up you do not reel past your float so the leader does not go through any eyelets. So that potential issue is ruled out.
20lb Maxima UG leader definitley should NOT be breaking. I typically run 20LB mono mainline (UG or similar...currently using Berkley Prospec, like it a lot), and max 15lb mono leader (I like Maxima UG or Berkley XT). Typically I run 12lb leader because, and as others have pointed out, if I foul hook a fish, or hook a snag, I want the LEADER to break, not my mainline (bye bye float, weight, etc). Sometime I'll run 10lb or even 8lb leader if the water is really clear but then I find more fish are lost due to teeth sawing through the thinner line. With 12 or 15 it rarely gets sawed through and I check it often, if getting rough/nicked up I tie on a new leader.
If I were you I would go into a fishing store (not crappy tire) during non peak hours and ask one of the staff to take a look at your knot where the line keeps breaking. Chances are they'll point out some issues with your knot and show you how to better it.
IMO for mono line to swivel all you need is the improved clinch knot. Easy to tie and reliable. If you like farting with knots there are lots of others to try