Has anyone added an electric igniter to their gas burner, to start or restart by button press their burner? Bolt it to the side, so the igniter is just under where the flame is, and the button is on the leg of the burner. Something like this MENSI Double Ignition kit Electronic igniter with high Spark Plug Wire Length 450mm Each for Catering euqipment Stove https://a.co/d/aPxAqWn
Usually if a flame goes out you should find out why and resolve that, not just try to light it again.
Wind barriers? Assuming it's wind that's blowing it out.
Otherwise, I'd be looking at some furnace components. A flame sensor to detect flame, and if no flame is sensed, it would close a relay to power the ignitor. I've never personally wired one up as it's the opposite of what a flame sensor is typically used for. This also will most likely require more then a 1.5v battery or a 9volt. Plus you'd need to find a way to close the relay after you lose the millivolt reading from the flame sensor.
Long story short, it's possible but not fun nor easy and you'll need a bunch of electrical. Manual intervention will most likely be the route you take though
Have fun and don't blow yourself up