For the OP: If it were me I would consider purchasing a regular, appropriately sized breaker and replacing an arc-fault breaker that often trips with it, just long enough to see if it solved the problem (i.e., run those programs 8 or 10 times). You could then look for alternate (perhaps newer or different manufacturer) arc-faults and get both Insteon reliability and better protection. But if you are not familiar with how a breaker trips, then no offense but you don't need to be working inside a panel. So call an electrician, have all parts on hand (such as replacement arc fault breakers that fit your panel but from a different manufacturer) and explain the problem and your goal to him. With proper planning you can likely resolve this ine one visit.
Also, these MAY be GFCI breakers, which take the place of a GFCI outlet as first outlet in a circuit. Do NOT remove GFCI protection! You can determine whether they are GFCIs with a $10 device from a home center that would be good to have around anyway. It might also be possible to add a GFCI outlet that would do the same job as the breaker for GFCI protection and use of a regular breaker, but I agree with others that this is lkely an arc-fault breaker that is falsely tripping. Either way, I am not a fan of gerry-rigging by bypassing safety devices originally installed. This is likely solvable while retaining the protection these devices add because they are likely just operating out of spec - it's just a little bit more effort and expense to do it.
Re: the other comments in this thread on panels - We had an odd siuation when we bought this house, in that we had service split into two 200 amp panels. The left panel (not a sub) had only the heat pump on it, with three separate breakers for compressor, air handler and backup strips, and a lot of empty spaces, but NO main breaker! And monitoring was apparently done with CTs. The only thing anyone could figure out was that it was somehow designed to work with special pricing for heating all electric homes years ago (late 70's house), a practice that no longer applies here. Neither we nor our electrician had ever seen anything like it. And the big problem was that the right panel was so overloaded with circuits that it was difficult to get the cover back on because of the rat's nest of wires in it. We ended up replacing the heat pump panel (adding a main breaker, which made everyone including the inspector feel much better), and transferring several circuits that would not be needed in a power outage to that panel, freeing up space and resolving the rat's nest in the other panel. We then added a UL-approved manual transfer switch to a generator that allowed us to use most circuits in the house during an outage (not the heat pump, range, dryer or ovens, but but most others), along with whole house suppressors on each panel. All in all a decent sized job but the result was a much safer, more effective outcome. It's amazing what some builders do and get by with originally...