If your USB data lines are 1.6in long on the board and you did not take measures to ensure controlled impedance(thus probably violating the 100 ohms rule) then that's most likely the issue. Full speed with its reasonably low frequencies might still work well but the operating frequency of Hi-speed is around 50 times higher than full speed, and impedance does matter a lot at these speeds. The fact that the connection works with full speed seems to support that theory.
Maybe you could estimate your trace impedance with something like that:
http://www.eeweb.com/toolbox/microstrip-impedance and tell us your results.
Also, it's probably a good idea to try and minimize the trace length of the USB signal...
You might find USB routing guides helpful, like this one here:
www.ti.com/lit/an/spraar7a/spraar7a.pdfIt's in the guide and has been stated here, but I still want to stress this again: Never run any signals directly under a USB line. If you only have two layers, put solid ground there and that's it, if you have more layers, put a solid ground plane between your high-speed line and anything else(apart from the paired high-speed line, of course).