Why a solid state relay rather than a MOSFET?
Also, an SSR (whether MOSFET, IGBT, triac, or SCR based) doesn't latch either. Only some esoteric mechanical relays latch.
I had a similar requirement to OP, though my USB hardware was fine, it was a third party device that would sometimes fail to connect when the system restarted. A watchdog reset of the uC trivially reconnected my hardware, but I resorted to enabling/disabling the AHCI driver to force Windows to re-enumerate USB devices to get that to be reliable.