CA running problem

I had an issue with my B once were it was running on 1 cylinder...turned out to be the rotor not turning. It has a fairbanks mag so I am sure that isn't your problem.

Coming in on this late, but after reading your post, I had the same thought that Dick mentioned about the advance wieght or wieghts hanging up or a spring broken. As Dick mentioned, if you can feel the tension on the main shaft, and it returns smoothly, you're probably alright. If not, tear down the Distributor and check out the springs and weights functions. Many, many times when I do these Distributor rebuilds, the Distributor housing is loaded with rust dust and debris which will hang up the centrifical advance mechanism. After I glassbead things all up, I'll spray a few light coats of dry graphite on both sides of the wieghts so they operate nice n' smooth. You may want to renew the springs if the coils look stretched. The other thought I had was a vacuum problem. Possible vacuum leak somewhere around the manifold or in the carburetor being the engine runs smooth, then it goes rough and backfires. A lean condition will also cause that whether its carb related or manifold related. Give a little spritz of carb cleaner around the intake/cylinder head mating surface while the engine is running. The engine may smooth out if you find the right spot which would lead to a vacuum leak. Another way to check is pull the choke closed a fuzz and cut down your cfm intake and make your mix richer. If the engine responds to this and smooths out and runs smooth all the while the choke is partially on, its an air/fuel lean problem which could point back to vacuum again. Carb or intake.. You'll find it. It just takes some patients and troubleshooting...

Me, I would pull #1 plug. Hold finger over plug hole and turn over with crank until you feel it starting to blow compressin out #! plug hole.  put a piece of wire down plug hole and crank very slowly until at top dead center. Now pull distributer and check to see what terminal rotor button is pointing to. This will now be #1 plug wire. put wires on plugs #1 in that terminal and continue clockwise with #2, #4, and #3. It should then start and run on all 4. May have to clean or replace plugs at this point also. I really like autolite 295's. Also, even though it's distributer ignition, I would use solid core wires, not carbon core. Also, as stated before, before putting cap on permanent, make sure you try to turn rotor and make sure you feel spring resistance from auto  advance mechanism. Don't worry about finding something supposedly minor that you should have caught before. A couple years ago, I tuned up my 47 WC and three times in a row, had plug wires switched. Guess I can't count to four.

I had a C last fall with a magneto that had a stuck advance. They don't always stick one way or the other. This one would start timed at TDC and run like a fuel problem or wires switched. Put the timing light and could not fine the fire line with out changing gears for the rotor. Would not start after getting it running and finding the fire line with the timing light.  Put a different magneto on it problem solved. Only took a few hours of messing around with it.

I forgot to mention that the plugs are autolites, I know I have 275's in mine, but can't remember the number on these. 

I would try doing a compression  test i had a wd last yr that was skipping and it had a head gasket leaking between the cylinders .And a b that had a valve that was sticking did very similer things

 Is the gas good? Mine was acted the same way and I checked timimg,wires,plugs,carb & valves. Than I found out my uncle dumped in a can of gas+diesel mix.