Lots of thought come to mind but first I have to say, stop using starting fluid. It's ether. It was designed for starting diesels in VERY cold temperatures when the heat of compression is not enough to light off the diesel fuel. It's not a product to be used in gasoline engines. The worst it can do is wash the thin film of oil off of the cylinder walls and then you have the pistons and rings running on bare metal to metal. Quite often (as a mechanic) I would have cars coming in on the tow truck wreaking of ether and would have zero compression. We would pull the spark plugs and pour a teaspoon of enigne oil down the plug holes and turn the engine over for a minute with the plugs out, then put the plugs back in and the compression would be back up and the car would run, but after we finally got it going we would check the compression again and it woulf be marginal, like 80-90 PSI. the damage was already done. The only cure at that point was honing the cylinders and new rings.
That being said, now, if you have oil soaked sparkplugs and or a weak spark, a gas engine will fire up when ether is put to it. So, i would check the spark plugs first.
Second, check the ignition coils. If you have an old dry sparkplug, open the gap up to 3/8" to 1/2" and then place it on each of the spark plug wires one at a time and ground the plug base out to the engine and check the spark. It should jump a 3/8" gap with a nice blue spark. If it doesn't you have issues with the coils.
Third, if the spark plugs and coils are good, what about the compression? An engine with low compression will attempt to start on choke but may not stay running but will run when the ether is put to it, so check the compression. If it's over 110 psi, it should stay running. If it's less, then you really need to get to the bottom of the low compression.
Fourth, How the fuel flow. What you describe could be a result of a clogged fuel filter. It gets a bit of gas in the bottom of the float bowls and starts to run until it "runs out of gas". You ponder your thoughts and try to start it again and while you ponder your thoughts the carbs get a little more gas and the cycle repeats itself. So pull one of the gas lines off of a carb and check the fuel flow. you should get, I'm guessing, 200 cc per minute (6 oz) If not, it might be the strainer in the tank on the fuel valve or if it has an inline filter, a clogged filter.
That's my thoughts for now. Do these checks and let us know where you're at.
Kayboy