Flame keeps going out on ring

Your pilot flame should be blue with a small yellow tip, and it should cover the thermocouple (a small rod in front of the pilot light). If the flame is too small and doesn't cover the thermocouple, it may be adjusted too low, or you have low gas pressure or you have a leak in your gas line coming in to the heater. If the flame looks like a lazy yellow flame, you are probably not getting enough air to the flame. Check that your air openings around the pilot are not clogged up. If the flame looks like a waving blue flame then you probably have excessive draft at the pilot. If the pilot flame looks good and covers the thermocouple, then the thermocouple might be bad. Best of luck. I hope I have helped.

Same problem with my hob. I adjusted the small jets to their lowest setting in order to be able to simmer -impossible on the bigger jets. The problem is the vents underneath the hob. These can't be closed off so the problem appears to be in the design. The solution I have to use while I save up to by a decent German model is to open and close the cupboard doors underneath the hob very, very slowly.

There must be a blockage on the inner flame ring as the gas is not getting to the thermocouple .

That is food/grease buildup. Clean the holes. TURN OFF GAS to stove, then just clean the holes in the burners with a soft wire brush. Then turn gas back on and immediately relight pilot lights. If that sounds scary, call your gas company, they might come out and help.

The pilot light jet may have got a little bit of dirt or grit in it which is preventing it from keeping alight. Try probing the jet with a fine piece of wire to see it the blockage can be dislodged. You may have to unscrew the jet to clear it by blowing air through it. Make sure gas is turned off first before removing any parts.

The pilot light also has a thermocouple that allows gas to the pilot light while the flame is burning. If flame goes out it shuts gas off to the pilot jet. The thermocouple is bypassed by a switch during the initial ignition and once the thermocouple warms up after a minute or two of holding in the bypass switch, it should maintain the pilot. If, after cleaning, the pilot light keeps going out, it would seem that your thermocouple is faulty and needs to be replaced

it sounds as if the tap is partially blocked

turn of gas and check the drip leg for water

Your thermostat is broken.
I think the gas 5 wire or the heat limit
FOR THESE PARTS LINK
or what i would check first is the fuse on the blower housing which is a thermal fuse. A regulat ohm meter /resistance meter can do the trick. No resistance should be measured or very low on this fuse. If uninfinit restistance this one is broken.
It can also be the limit thermostat . Measure when cold. > low resistance.
This is another link for PARTS
Good luck

check the vent plug on the regulator.