In 2 stroke sleds look for leaking oil/grease as a sign it is in trouble. Spray some starting ether around the seal while it is idling and if the rpm goes up it is leaking. Leaking is a late-stage thing - she's about to blow if that happens!
You can check crank run-out as well - imbalanced crank can be one thing that takes out a seal. Cords from a blown belt can as well - you can look for physical damage.
For 4-strokes I am not sure. What kind of sled are you talking about?
1971 Yamaha GP 396. Can only get it to run for about 10 seconds. Have plenty of spark and cleaned the carbs. Seems to be fowling out the plugs with too much gas. I adjusted the carbs as suggested by one of the old sled websites. Have the air screw closest to the engine 1 1/4 turns out and the bigger one 1 turn out. The float level sight tubes are broken so I just plugged the hole and played with the adjustment on the bottom of the carb. Dont know where to go from here. Got 120 PSI in both cylinders.
Sorry - I am not familiar with these engines/carbs so I can't really help with specific advice...
In general if you are fouling plugs check for fresh gas, too much oil in mix, weak spark. I just read your other post - I am a little suspicious of the coils either bad or wired wrong.
I have an 87 El Tigre that would start and idle fine but kept losing power. Turned out that a bolt head had snapped off and was shorting out the coils. It had enough spark to idle but not enough to go anywhere! Poor spark can also leave plugs looking wet as it doesn't burn all the fuel.
Also if it runs for a while then dies check the entire fuel system. It may have enough fuel to run for a little then starve. Check vent lines in tank, fuel pump (if there is one), filters, etc. We had a '68 skidoo that had a rusted tank. It would run fine for about 10 min then die when the filter clogged up. Wait a little while (for the sediments to drop down) and it would run for another 2-3 min. New filter and we get another 12 min out of it...
If you are sure it is getting too much fuel slowly lean out the carbs and see what happens. Carefully of course so you don't burn up the engine!
Good luck and let me know what you find!
PS - you could also check out totallyamaha or dootalk (vintage forum) and talk to people that know a lot more about this than I do! I just figured I would throw out my little bits of wisdom so you don't feel like you are talking to yourself here...