Electronic ballasts have a habit of tripping GFIs when nothing is actually wrong. In electrical circles this is known as a "nuisance trip."
It is caused by harmonics in the power line, often during inital powerup or powerdown. It's somewhat random, depending on a huge number of factors. Replacing the GFI may or may not help, and even replacing the ballast may or may not help. The harmonics can confuse the logic circuitry in the GFI, causing it to erroneously trip.
One thing you may try is putting a high quality EMI filter between the lighting system and the GFI. If you have a separate timer, you'd plug the lights into the timer, then install the filter between the timer and the GFI. This may stop the problem... or it may not ...
The type I'd try to get is made by Tripp-Lite, under the ISOBAR name. One of their smaller models, such as the ISOBAR2-6, would be what I'd try. ISOBAR units are expensive, I think the MSRP on the latter one is like $60, but you can usually get them far below that by poking around online or on that famous site where you bid on stuff.
Keep in mind that these units are often marketed as "surge protectors" but the surge protection is not what's important, it's the EMI/RFI filters that matter, so don't try to go to the store and pick up a surge protector, they will not help unless they have that key function. Also keep in mind that doing this may not solve your problem. You pretty much need to try it and see.
If that doesn't work, the only alternative would be to run your lights without GFI protection, but this should be considered a last resort if you have no other options.
