Why would my Tao Tao 50all of a sudden just die and won't restart

The most common things I have seen are fouled spark plug, bad gas, or bad battery. Give those a try first. If you still have trouble read on...

The way I start with diagnosing a Chinese scooter is with the acronym F.A.S.T. which stands for Fuel Air Spark Timing.
1. Fuel- is the fuel entering the combustion chamber? You will have to follow the path from where the fuel goes in, to where it comes out. The easiest place to start is by simply starting the scooter a few times, pull off the spark plug and see if the plug smells like gas or is wet. If you have a wet smelly spark plug, proceed to number 2. If it's dry, continue reading. One problem I have seen on low mileage scooters with a non-starting condition is debris from the factory that has clogged the carb. But before you start tearing apart the carb, look at the outside bottom of the fuel tank, there should be a fitting with 2 hoses coming out of it. One provides fuel to your carburetor, the other provides vacuum from the carburetor to the fuel diaphragm located at the bottom of the tank. Take the smaller and more supple of the two hoses off the carb. This is the vacuum line, make sure it's dry and not full of gas, and suck on it a little, do this several times and the diaphragm should start allowing fuel to the carburetor. For the more squeamish, get a syring for measuring oil from the auto parts store and use that to suck on the hose if you don't want you lips getting dirty. Give it a start, if the plug is still dry, pull off the fuel line from the carb and see if fuel is coming out. If fuel comes out, you might have carburetor issues, and that is another question in itself.
2. Air- Air leaks can cause all types of problems, start by making sure the boots from the carb to engine are snug and in place. If their is an air leak in the head or case, you will have to do some further research.
3.Spark- take the plug out, preferably in a space where it's dimmly lit so you can see a spark, in a pinch I have draped my jacket over my head and the engine and checked for spark on the side of the road. Now connect the plug to the plug cap and place it against the metal of the engine and you should see a spark. Nice bright blue. A weak white or no spark at all, start out by replacing the plug. If it still does not work, the most likely culprit is electrical shorts. If you suspect a short, start asking questions about scooter short, or kill switch short.
4.Timing- it is set and fixed on most scooters and it only gets out of whack when someone takes the stator plate off. Highly doubt this is a timing issue.