Re: 55 HP Johnson runs but then quits...
Hi there,
Just to warn you I only have a years experience on outboards myself so take what I say with a pinch of salt! The issue with this motor could be one of many of things.
I have a mid 70's Evinrude 55hp and have had similar problems to those you describe. I rebuilt the fuel pump with a kit from OMC as a first port of call as well as re-building carbs with kits along with full clean of the jets, new fuel lines, new hose clamps and a new fuel tank. I'd suggest an old outboard that runs a bit rough would benefit from these things as part of a normal service anyway so factor those costs in.
In the end our problems extended beyond this to a sheared woodruff key on the crank. Pull the flywheel if possible although this can be a day long job or more from my experience. Our crank and flywheel were badly damaged so our motor is now pretty much scrap but we get by with a heavily tightened flywheel nut and prayers. This is not adviseable by any means and we will probably shear the key any day. We carry a spare 4hp outboard for that day!
We also had a dodgy power pack which may have caused intermittent issues? I don't know but its been replaced now. Timing was also out and was set using Joe Reeves' guide to WOT timing.
Engine runs well now and doesn't quit.
BUT the issues described for your motor could be completely unrelated to my issues, I'm sure one of the experienced guys will be able to help you more than me. When engines warm up they can expose underlying faults with electrics and other things.
Good luck, just offer him the list above and minus it off the asking price!