If the VFD is shutting the motor down due to load, it should give you an "OVL.d" error on the VFD display.

No errors on the VFD? Just the VFD shutting off completely? Not an overload condition. VFD doesn't power itself off in that condition.

The spindle door microswitch will make that happen if it is a bit loose. Maybe it is vibrating under load. Also (as others suggested), a lose power connection to the VFD or lose control wiring on the VFD could do that.

Does it sound like the motor is noggin down and slowing just before the trip?