Thanks!
I fixed it by following your advice. The thermocouple was bent backwards on the left burner, probably because of cleaning/scraping some grease with a knife at some point in time. Additionally, there was some dried up grease underneath the top plate on the left burner which prevent propane from easily going to the side where the thermocouple is located, so the flame didn't burn on that side ...
I cleaned the underneath of the plate so now the flame forms a nice circle again and bent the thermocouple straight again. The flame now stays on by pushing the button only for a few seconds!