It is not terribly uncommon for "electrical noise" to trip a gfci breaker, according to my fellow pool techs. I ran around in circles a while back trying to find the source, as the pump was tripping out every few days. I can't tell you to do this, but in my case, as well as all the techs I spoke with, the solution was to replace the gfci breaker with a standard one. No issues since.
A master electrician friend of mine said that as long as the pump is the only load on the breaker, the gfci is superfluous. The acid test would be to temporarily change the gfci breaker to a standard one. If it still trips, there's something else involved, get an electrician.