Could you swap over S1 and S2 and tell me if the problem moves position?
I suspect the hold-on functionality internal to S2 is defective which means only the pull on coil is doing any work to operate S2 - but the pull on coil becomes de-energised when the power contacts S2 close - so to keep the power contacts closed the hold-on coil must be energised. Check the coil resistance of S2's hold on coil. Check it has 110V to energise it - if it does not then trace the control wiring to it backwards to find out where a Normally Open contact is not being closed.
Or something like this - off to watch the apprentice now. Will look again afterwards.
I suspect the hold-on functionality internal to S2 is defective which means only the pull on coil is doing any work to operate S2 - but the pull on coil becomes de-energised when the power contacts S2 close - so to keep the power contacts closed the hold-on coil must be energised. Check the coil resistance of S2's hold on coil. Check it has 110V to energise it - if it does not then trace the control wiring to it backwards to find out where a Normally Open contact is not being closed.
Or something like this - off to watch the apprentice now. Will look again afterwards.