I've noticed one weird thing with the TD-11, and I can't tell if it's my computer or the DAC. If I leave my computer on but shut off the DAC at night, then power the DAC up again the next morning, I get nothing but static from the USB connection at first. Over a period of about ten minutes, the static fades and the music starts coming through. There's no such problem from the SPDIF connection. Go figure.
I've had different issues over the years with various computers and their USB connections. Does your computer go into sleep mode or hibernate mode or anything like that? In my experience, sometimes the system has problems reestablishing or maintaining USB connections after waking up from a low power state. It's especially problematic with devices that draw their power over USB - I had a pair of compact speakers that just would not reconnect no matter what. Required a complete restart. But even some AC powered units have had issues.
Can you disable the hibernate or sleep function and see if that helps?