It is important to investigate what the cause is for that happening. Some faults might lead to breakdown. There are some troubles that regularly pop up on these engines.

First check if the crankcase is dry or overfilled with oil. Some oil should (in my opinion always) leak out when removing the level plug, from a few drops up to say...1/3 cup or 0,75 deciliter. Be aware that an open hand pump petcock will likely leak oil into the crankcase during run or even standstill, the ball valve in the pump check valve isn't reliable.

Next check if the compression is equal on both cylinders. Then check if the intake nipples is leaking at the threads, rivets or ferrule. Make a simple tool and do a bubble test, that's important.

http://virtualindian.org/11techleaktest.html

Next common problem is..

Is the plug really igniting all the time on the colder cylinder or is sparks going between the leads. That can be checked with a induction timing light hooked up to a ordinary 12V battery but a better measuring tool is an oscillator. Should also be checked with some load and higher revs on the engine. Is there carbon tracks or sparks migrating in the distributor cap, or maybe a intermittent short somewhere inside the magneto? In a ordinary 4 cylinder car engine it is hard to detect with senses up to some 20% misfiring! Wrong plug gap makes ign. misses. Should also be about .020-.025"(0,5-0,6mm).

If the compression values was low or unequal, check with a leak-down tester the condition of piston rings and that the valves are sealing properly. A very handy tool to have in the shed.

https://www.youtube.com/watch?v=PZAxqvA9kKE

A quick check can also be done without a meter to just get a indication if there is a problem. Just lock the engine in TDC. Use the hose from the compression meter, put compressed air in and listen where air escapes, exhaust, intake or crankcase. Do the same on the other cylinder and compare.

The questions continues... Unequal ignition timing. A worn ignition cam, or for example a 45 degree cam installed instead of the proper 42 deg.cam. Wrong breaker gap makes ignition missing. .016"-.020" (0,4-0,5mm) works for most magnetos. 

Remove both heads to check timing, on both cylinders. 7/32" (5,5mm) before top dead center for the 37ci engine and 5/16" (8mm) for the 45ci engine. Too late (closer to TDC) makes the exhaust hotter. Too early (further before TDC) makes the cylinders running hotter.

With the heads off it is time to check if the valves are opening to the same height, about 0,26" (6,7mm) (I think!). And are they timed same on both cylinders? With original cams, intake opens some .34" (8,6mm) before TDC and exhaust .502" (12,7mm) before BDC. Wear can change things rapidly.

Is any of the valve springs weak or broken? A fresh orig. spring should have about 70lb (32kg) seat pressure. And if the compression values was unequal, check that both pistons rise to the same height, it's funny sometimes to find unmatched parts assembled, or perhaps bent rods.

Signs of piston seizure? Does the engine turn smoothly all 360 degrees around? Piston pin seizure can in some severe cases be felt, the piston is rocking from side to side at TDC and BDC when the crankshaft is turned.

Carb problems is another, adjusted too lean, clogged jets, wrong parts or wrong assemble, or wear. A leaking float valve can result in a too lean adjustment of both high and low speed jets. 

If everything else is up to specifications, a larger air leak at the exhaust nut can make an afterburn of unburnt gas in the hotter tube.