Check the voltage provided as a parameter in the USBFS_Start(uint8 device,uint8 mode) API function. If the board is powered with a 5-V supply, the argument mode must be assigned as USBFS_5V_OPERATION. In this case, the internal regulator is enabled. If the board power supply is 3 V, the macro USBFS_3V_OPERATION must be used. If the supply voltage is unknown, it is better to use USBFS_5V_OPERATION because in this case the internal regulator is enabled.
Also please have a look at the KBA: Troubleshooting PSoC® 3, PSoC 4 L-Series, and PSoC 5LP USB Designs - KBA210620
The problem is with USBFS version 3.20. A simple downgrade to 2.80 fixed this issue with no change to the code.