I have 3 Fuze v2 and 1 v1, and all of them freeze and turn off when files are written to the device (but not during constant reads, strangely). Digging through the Rockbox forum, I found a mention that sometime after Rockbox v3.9 the USB got a little quirky.
Try installing Rockbox release 3.9 (it may break a few themes) and see if it stays connected. Otherwise, if you don't have a microSD card bigger than 4GB, you can boot into the original Sansa firmware (hold << while powering on), connect in MSC mode and sync that way.