I called in our electrical contractor since we were stumped and he told us that a GFI can "see" a ground fault even if it's on the secondary side of our transformers.
Nahh, that's jibberish.
The GFPE (Ground Fault Protection for Equipment) Main Disconnect you are dealing with will only sense a "Leakage Of Current" on the 480Y/277 VAC System ("Side").
At the MSB (Main Switch Board) - where the GFPE Main Disconnet is located, all 4 Conductors of the Load Side Feeder (ØA, ØB, ØC, N) are routed through a single C.T., which is coupled to the trip circuitry. The trip logic reacts to Amperage levels from the C.T., which are produced from Zero-Sequenced Current levels in the Feeder.
GFPE or GFI devices do not "See" Ground Faults - they only react to an imbalanced current flow on the circuit(s) run through their C.T.
As to sensing the Secondary side of an Isolated Transformer, if the Primary Circuit is complete - without some type of L-G leakage, then there would be no imbalanced flow, and no way to have the trip logic sense an imbalance - even if there was a bolted L-G fault on the Secondary side.
A few things to check regarding the GFPE trip would be:
[*] Insulation Breakdown,
[*] Randomly occuring Arc Fault,
[*] N-G connection downstream of the GFPE,
[*] A Motor which is infrequently used, which has a fried Winding - or Windings,
[*] A Transformer with one or more Primary Coils leaking current to Ground - or possibly arcing to ground,
[*] Some 277V Lighting Circuit, which has a Ground Fault on the Load side of a switch - so when someone throws that switch, it causes the GFPE to trip, and the person responsible for the "Major Power Outage" throws the switch back off, then quickly vacates the area,
[*] The GFPE is "trimmed" way too low - meaning the adjustments are set to the extreme minimums on all settings, and the device is simply reacting to normal power quality issues - like hard starting Motors on very long circuits, lots of Fluorescent Fixtures on very long circuit runs, etc.
Good luck shooting trouble on this.
Let us all know what the outcome is.