UCD9090: GPIO Shutdown

That is helpful, but is there a way to make the device stay off until a power cycle if one of the pin selected rail states is changed?

Why not used UCD9090A. it is pin to pin compatible with UCD9090 and it has a GPI fautl shutdonw feature which can meet you requirement.
GPI fault shutdown is to shutdown the rail and keep the rail off even the GPI is flipped late on. This is slight different with PIN SELECTED RAIL STATE.
But under UCD9090, If you want to use GPI to shutdown rails and not re-enable rails when GPI is flipped, you have to burn a MON pin to monitor the GPI and treat it as a UV fault. Do you have spare MON pin to achieve this?
Regard
Yihe