Controller Is Constantly Disconnecting

I've had my Xbox 360 Les Paul guitars since GH3 came out back in '07 and I've been trying to bring them back to life. I've hardwired the fret buttons to the main pcb so that I don't have to deal with those stupid pogo pins, but I've run into a bigger issue. It keeps disconnecting, inconsistently at that. Sometimes it's every 30 seconds, and sometimes it'll go for a few songs without any problems. It always disconnects for either just a split second, or up to 30 seconds. ⏎
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I've changed the 220uf 10v cap on the battery pack, and the problem is still happening. I'm not sure what to do at this point. Anyone have any tips?