EMC, resistors and trimpots
An ESD test to the adjust screw of a trim pot would not normally change the mechanically adjusted value or value of other fixed resistors.  If your equipment malfunctions when the ESD test is administered then the fault may lie else where, such as the ESD charge getting into other circuitry, or the charge not dissipating to an earth ground. 

A solution might be to find a similar trim pot that has a plastic (rather then a metal) adjustment screw.  Yet another possibility would be to put the trim pot further into the assembly and have a plastic extension piece to the screw.  If the ESD test shows an error that simulates a fast trim pot change then you might be able to adjust your software to temporarily disregard any fast changes.