I had the same problem at the beginnig, this is how I solved it:
1) Wash it under running water, with soap, after each time you exercise or sweat. Rinse it thoroughly: chances are that the soap or sweat will give you more rashes than the watch itself.
2) Don't wear it on exactly the same spot of your arm 24 hours a day. What I do is wear it normally during the day, then, before I go to sleep, I put the band in a larger position, and move the watch upper on my arm, so that it will stay firm on my arm, but not on the same spot where it stays during the day.
Also be careful that no soap gets between the watch and your arm like when you wash your hands. If it does, rinse the watch and your arm with water to remove all the soap.
Replace the strap. I swapped to nylon (the original Garmin Ultrafit) and no problems since then. I wash it maybe once every 2-3 months and it seems to be enough.
