Coming back to this one — we had another position deviation mystery last month that's worth sharing. Press was throwing the fault only on one specific die, and only after about 200 cycles. Turned out the ball screw was developing a thermal preload issue.
Here's what was happening: the ball screw heats up during continuous running (ours was hitting 45°C after 20 minutes), the thermal expansion increases the preload, and eventually the motor can't push through the added friction at the bottom of the stroke. The deviation would spike to 0.04mm right at BDC — just enough to trip the alarm.
Diagnosis was simple once we knew what to look for: put a non-contact IR thermometer on the ball screw nut housing. If it's climbing past 40°C and the faults correlate with temperature, that's your answer. Fix was adjusting the preload spec from the factory-default 0.03mm to 0.05mm to allow for thermal growth. Haven't seen the fault since.
The other thing I'd add to what anna_plc said about gains — if you're on Yaskawa, check Un025 (torque command monitor) during the fault. If it's hitting 100% at the moment of deviation, the motor is genuinely torque-limited and no amount of gain tuning will help. You either need to slow down the forming segment or you're undersized for the job.