I was just going to say it's probably become gummed up but then read on ... It's worth a try with some industrial meths and a good burner (decent sized wick as Jan Ridders suggests) - some people use glass fibre wicks that don't burn and produce sut.
Another bone of contention is that I and a few people use oil (I use car engine oil), it takes longer to warm up (about 10 mins) but I find the contaminants are pushed out in the oil and it provides a better seal for my not so good machining! Some peoples are probably made to a higher standard, finer tolerances on the piston and valve which mean oil anywhere near it causes too much friction in the system, Engine oil gives very low friction once up to temperature though. Just a thought if you're still struggling. I'm actually thinking of putting an oil cup at each end of the cylinder on mine, like 'poppin' but 1 for the valve and 1 for piston as it causes a bit of a mess.
I just soft soldered an end in a bit of tube for my burner - it doesn't get hot, with a push fit cap for the top, simple but effective, the way I like it!
Nick