As with most things there are a number of possibilities. As you say, the most likely is carbs. I can't remember whether the RD200 has an off position on the fuel tap. If it has then try the following:
Run the bike on the stand for as long as it will go for. The second it stops, turn the fuel off. Remove the float chambers from the carbs and see if there is any fuel in them. It could be that the fuel is taking its time to get into the float chambers due to a blocked fuel tap filter or gummed up float needles. By doing this test you should quickly establish that fuel stavation is the cause.
Another possibility, though much less likely, is that the exhausts are so badly clogged with carbon etc that the pressure is building up and stopping the engine.
I would suggest you check out the following website as you are bound to find the answer to your problems there.
www.aircooled-rd.comJust had a further thought:- Before you try the above, undo the petrol tank cap whilst the bike is running and see if it keeps going. If it stops, no harm done anyway but if it keeps running then your tank's air vent is blocked. Don't try restarting the thing with the cap undone because you'll end up splashing fuel everywhere. It could suddenly get very warm!