Hi geoff, I had the same problem on one of my om2n's. A chrome one, strangely the black ones have been fine. I don't know how mechanically minded you are? but the fix is relative simple if annoying because that body did it several times when i dry fired it until the problem was cured. You'll be glad to hear it has not let me down since.
From memory now,to fix the problem, first remove the battery cap,batteries and bottom plate of the body(i put the little screws in a jar). Now keep the camera upside down and while moving the advance lever gently back and forth (it will only move a few mm anyway) look to the right hand side of the mechanics. You should see 2 bars(with hooked ends) moving in unison, one above another latching onto some teeth on a cog? gently move them out and away from the teeth on the cog (i use the smallest precision screwdriver i have), this should now have released the cog so it can turn , you should be able to advance the lever the full length of it travel? do this and stop.Let the prongs fall back into position. Now replace the back , replace the batteries and 'reset the mirror'. The shutter should now fire and the advance lever advance correctly.
Unfortunately for me the first time I did this, i found that the shutter froze again unfortunately and I had to repeat it a few times. I quickly got into the habit of test firing it while it was still upside down, balancing the the bottom plate with batteries and executing resets. It was annoying but it worked.
I don't know about yours but my chrome body started having this problem after I used the self timer. The other thing i found helpful with this particular body was to press the shutter button incredibly gently, lifting off the moment the shutter fired and not depressing the button all way down or hard, and moving the advance lever in one smooth fluid motion( not too softly and not too hard ) helped too.
The om2n really is a great body and one of my favourites along with Canon T90 and Pentax Spotmatic F.
Hope this helps. Any problems I can give you my number etc . . . Good luck!