One more thing on F07801/F07802 that bit us last year — check your S120 firmware version. Siemens changed the overcurrent detection algorithm in V4.7 SP2 and it became more sensitive to current spikes during reversal. We had a press that ran fine for 2 years, then started throwing F07801 every 200-300 cycles after a firmware update during scheduled maintenance. Nobody connected the two events for weeks.
The fix was adjusting p1520 (current controller adaptation) from the default. Siemens tech note 109763694 covers it but good luck finding it on their support site. If you're on V4.7+, set p1520=1 and see if the fault frequency drops.
Also — F07802 specifically on press applications: if it only triggers during the return stroke at high speed, check your DC bus voltage with a scope during that phase. The motor is generating back-EMF during fast return and if your regen resistor is undersized or the chopper threshold (p1254) is set too low, the bus voltage spikes and triggers the fault before the chopper can react. We bumped p1254 from 760V to 780V and added a second regen resistor in parallel. Problem solved.