The relay pair on the right is probably an 'excluding' type interlock... which means it's either Y-D start, or a direction-reversing circuit. The mechanical interlock prevents one side from being closed while the other is closed.
Check the plunger switches per Zig's comment (make sure you don't have an errant signal holding one relay high). A giveaway, if it's stuck in one mode, is to check-see if the interlock bar is toggled in one direction, but the coil is not energized... if you see that circumstance, it means the mechanicals are simply stuck. IF the coil is energized, it means you've got a control elsewhere that is still energized when it shouldn't be.
Gut feeling is that the limit switches are 'snap action'... they have an overcenter spring type mechanism, and if they're glopped up inside, they're not returning after being actuated... opening, cleaning, and reassembling will fix that.
If it really IS the interlock mechanism, then disassembly will reveal dirt, crud, and worn spots. Dressing the worn spots on pivots and fulcrums, cleaning burrs from the sides of wear surfaces, or making new bushings for worn holes will do well after cleaning corrosion. A brief visit from a wire wheel frequently works wonders... a dremel with one, and another with a white stone will resolve many ails.
The only other thing that comes to mind, and it doesn't happen often, but can...
IF the polepiece of a contactor winds up in the path of a strong DC discharge, it can become magnetic, which can cause the contactor armature to 'hold' when it shouln't. Typically, AS will de-gauss the circumstance, but not always. Not likely, but a non-magnetic screwdriver touched to the polepiece with no power will tell you... if it sticks, it's been magnetized. Don't think it happens on machine tools much, but I've seen it happen on trains when an axle grounding shoe went bad... traction current took a different path...