Where is your car located with respect to your breaker panel?
What can happen is a voltage differential between the local ground the EVSE is using and the actual place where your ground rod is driven for your property. If there is any current flow from your wet car into/out of the ground that is greater than a few milliamps, it could trip the GFCI protection. (depending on how the EVSE monitors for faults)
If these "nuisance trips" continue, you should check for a voltage differential. If it exists, you may have an inadequate ground system in your house, or the ground rod may be too far away from your charge location. If that is the case, you may have to install a local ground rod.
It could also be a nearby lightning strike that ionized the air enough to create current flow through the ground.
Of course it could also be that the AV EVSE sucks! =) So far there has been one failure documented, and from the looks of the insides, I would not doubt this.
In my opinion, on GFCI fault the EVSE should immediately shutdown then sound an audible alarm, wait a minute or so, then try to restart. If after a few attempts the fault is still present, then it should go into lockout until a user resets it. The audible alarm should continue however. This would probably eliminate a lot of nuisance trips and upset owners finding their car uncharged in the morning.