What about pests of the two legged variety?

How many plants are missing? Are any still there but partially chewed? How often are you checking the area?

I hate to tell you but sonic pest repellants are not very effective despite the all the publicity the manufacturers produce. Scent and/or taste repellants tend to be more effective but even those not 100%.

Did you plant the begonias with any sort of fertilizer like bone or blood meal or other organics? That could be the culprit with raccoons.....they could care less about the vegetation but would dig for the smelly ferts. If that was the case, you should see the plant remains around. Otherwise I'd guess maybe bunnies (if present in your area) or deer. Or as Dorie suggests, possibly humans :-))