Hi Grant,
When is the last time your bike was serviced? However it does sound like it has some sort of fuel problem? By travelling a short distance, then cutting out, it's like the engine is using up the fuel in the carburettor faster then it's filling up.
Here's a few things to do check,
1) Next time the bike is running & then cuts out, quickly loosen the petrol cap & listen for air being sucked into the tank, you might have a blocked fuel cap which is causing a vacuum in the tank thus stopping petrol getting to the carb.
2) If the bike has a fuel filter, have a look to see if it's full of crud,
3) When you have the engine running, pull the petrol tube off the carb & catch the fuel in a container. Check you have a nice flow of petrol. If not you could have a blockage in the fuel tank or the fuel pump maybe faulty.
4) Clean the carburettor, small engines like the SR have tiny little jets in the carbs which clog up very easily as well as being exposed to all the crap thrown up from the road as they're so close to the ground. Also clean or replace the air filter depending on the type of filter. Fit a new sparkplug if the one in it is old.
After doing what I've recommended, I will be very surprised if your bike is not going 100%. Keep me posted & tell me how you get on.
Steo, November 2009