I would check if the VFD has a parameter you can set that requires periodic messages from a controller to stay active.
Mine does, and I configured it that way, but it also needed me to wire up a reset button to provide a momentary on/off.
I wrote up my settings here Optidrive E3 VFD - #3 by AndyP. Look for “purpose 3”. Your VFD may have a similar parameter.