Mouse on mac mini quits for no reason.

For security I keep my Mac offline unless I need to go online. I have no issues offline. When I'm online, my mouse will frequently stop working. The cursor is still there, the light on the bottom of the mouse is lit, but the cursor will not move. I have to disconnect and reconnect to make it work. Again, that does NOT happen when I'm offline. I'm afraid it might be malware or something even though I'm using standard anti-malware progs.