if the mechanical shock of the reset bar is tripping the relay, then you'll want to look for wear on the armature plate and the roller lifter arm. Also look for dried grease that may be preventing the armature plate from latching the relay.
if it looks worn, you can swap the pieces with another trip relay that would be less annoying if it trips and see if the problem moves ... then you'd know for sure it's time to source some replacement pieces.
a less common problem is crud on the coil top/armature plate that is causing the plate to stick to coil top ... at least enough for the relay to not reset reliably. However, it sounds like your problem is the relay is tripping when it was already latched/reset, so it's not that (assuming you do howard's test to verify it's not electrical).