Get a torch and do a test
Hold the torch to the pilot assembly and see if the flame stays on. If it does then repositioning the copper/nickel probe on the pilot light may make it stay lit. For optimum performance the flame needs to hit the very tip of the bulb. The copper/nickel bulb when heated produces electrical current which opens a bi-metal flap inside the gas valve. You may just have to replace that safety valve if that flame will not hold. Some times buildup on the pilot itself will make the flame smaller. Don't try to open the pilot hole but instead try and clean it with a wire brush or some rustbuster.