1986 shadow vt700

[caz.k]

Hi, I recently bought this 86 shadow vt 700 in the summer and i have been trying to fix it since.... when i reach speeds of about 55+, my back cylinder shuts down, and eventually, the whole bike shuts down. once i pull it to the side of the road it will usually start back up and work fine after a couple of minutes. The bike has a pair of straight pipes on it, as opposed to the stock mufflers, which at first i thought was the problem and it needed to be rejetted, but i was told this was not true and that the problem was most likely electrical. I cleaned the carbs, replaced the stator and regulator/rectifier, and i have a new battery on the way. i changed the stator and regulator rectifier today and i still have trouble. I also switched the two coils to opposite cylinders and the back cylinder still shuts down. Im stumped.