If your
propane hoses hang in a "U" shape from the regulator downward and then back up to the tank shutoff connection disconnect the hoses at the regulator. Once off, let them dangle downward with the open end in a clean pan, shallow dish or something similar. Leave it that way for a while and see if any oil dribbles into the pan. If oil is present in the pan then you've found the problem. (All propane has some oil in it to help prevent the inside of tanks from rusting.)
I had occasions when my propane bottles were overfilled which can cause excess oil to settle into the bottom of the "U". When you start your stove (or other appliance) the sudden rush of propane gas pushes past the oil settled into the bottom of your hose and appears to operate normally. As soon as the initial rush of gas subsides into a state of normal, trickle level use, the excess oil resettles to the bottom (lowest area of the hose) and blocks normal gas flow from getting to where you need it. That's why the initial flame gets smaller or simply shuts off.
The lesson cost me install time and a new regulator but that's OK, now I have two functioning regulators. One is now a spare.