Your experiencing fouled plugs. Fouled plugs have carbon buildup that grounds the electrode of the spark plugs over the ceramic with carbon. The carbon buildup occurs because the AFR (Air Fuel Ration) is too rich. This makes the combustion process, when you fuel is burned, too cool. Since combustion is too cool carbon buildup occurs on your sparkplug and now you can't start your scooter.
There are a few things to check and most of them involve cleaning up your carburetor and your air intake.
Validate that the NGK sparkplug that your are buying is the correct one for the scooter. If the plug is too 'cold' because it is incorrect you can experience plug fouling.
Clean your air filter. Make sure it's not too restrictive. You best bet is to replace it if yours is dirty and clogged. Purchase a foam air filter you can clean and re use if they are available.
Points are cheap and the condenser can go bad and not provide enough electricity to your coil to have a good spark. A good way to eyeball if your spark is bad is to remove the sparkplug from the scooter and put it in the end of your sparkplug wire. Allow the sparkplug to rest against the engine of your scooter so it's grounded and turn it over. If the spark is orange you have an issue. If it is whiter or blue, it's fine and don't worry about the points.
Make sure your floatbowl on your carburetor isn't leaking. If it is, it can fill your crank case with fuel and when you run the bike it's adding additional fuel to your mixture and fouling your plug. You would need to remove your carburetor and then your floatbowl and clean out the carburetor with carburetor cleaner. Use the little red tube that's provided with the can of compressed carburetor cleaner to squirt into any brass jets your have as well as your carb needle and seat where the fuel can leak into the system from.
Once you have it put back together make sure any vacuum lines are reattached to their proper nipples so you don't develop a lean condition from an unmetered air leak.
If you have additional questions, please open a new one. Remember, you are getting too much fuel from either an a restricted air flow or a carburetor issue more than likely. If you need direction on timing the scooter because you want to replace your points, that's an entirely new question and feel free to ask.
- As @sweber states below in his comment. Check that your choke is not sticking. Your problem could be as simple as that.