Very interesting. Your issue prompted me to study up on these breakers as I had not heard of them before. I am sorry that I cannot offer any direct experience. Hopefully some of the x-10 experts will have an answer for you.
From what I read these devices have to be fairly intelligent to be able to determine the difference between normal arcing that occurs when plugging and unplugging inductive loads and inrush currents from an actual fault. They are supposed to be looking for irregular currents near the zero cross point of the sine wave as well and this is where x-10 transmits. I could not find anything about whether or not they might filter the line with a capacitor or anything that might suppress an x-10 signal. Since these breakers are also looking for a "noisy line" that might indicate an arc-fault I would think that they would not filter the line much. They may include a filter it to attempt to make it less likely to nuisance tripping.
Good luck with the repeater as that seems like possible solution. I hope you will post your results so we can all learn from you.
