Check all your hoses to make sure there are no air leaks. RSTs don't like them due to mechanical fuel injection. Would prob still have problems with no load too though but check anyway.
If your fuel pump is worn would also do this. They often get quite noisy when on last legs. A garage should be able to check your fuel pressure for you or you can buy a gauge and check it yourself if confident. Fuel pressure should hold good throughout rev range but with kaput pump it will drop off causing engine to die like running out of petrol.

It could could be quite a few things to be honest though but worth looking into those two for starters.