Often, when I plug my phone into my PC to transfer files, I get the 'Phone charging slowly' message. OK, I wasn't trying to charge it, but I can handle the message.
The problem is, that invariably, when I get the message, the phone/PC fail to connect at all.
Partial/tentative answer: I think it may depend how charged the phone is. After leaving the phone charging for a while, I tried unplugging/plugging and it connected.