First thought would be incorrect L-N Terminations at the GFCI Receptacle (Line side Grounded Conductor Terminated to the Load Terminal / Load side Grounded Conductor Terminated to the Line Terminal - and/or a similar scenario for the Ungrounded Conductors)
Next would be N-G connection on the Load Side of the Devices; could be from a nick in the Conductor's Insulation - resulting in an N-G "Leak",
could be from bare EGC touching the Silver Screws on the Device,
Etc...
After that would be Wiring Fault - Open Common Neutral issues, Neutrals of the Two Branch Circuits tied together at some remote location past the GFCI Device, etc...
IIRC, the latest and greatest GFCI Devices are supposed to "Crow Bar" (trip and remain non-resettable) if the Load Side has a Wiring issue.
Then there is the possibility of Current flowing via either of the Two Wires of the Branch Circuit - which is causing the Devices' CTs to sense an imbalance...
Last would be defective Devices.
Start with the "Obvious" and easiest, then work your way down the list until you reach "Defective Devices".
If you get that far, exchange with a Device which is known to be functioning properly, then energize the Branch Circuit to see if the properly functioning Device will hold or trip.
To verify if Neutrals for the Two Branch Circuits are tied together "Downstream" of the Devices, turn on One Circuit at a time. If no trip occurs, turn on the Second Circuit.
Trip will indicate a Load Side Wiring issue.
-- Scott (EE)
