Lennox HE propane furnace
I will assume it is indeed a failure to ignite problem. The way it works is your circuit board puts out about 5 milliamperes through to your flame rod. When there is flame the electrical signal jumps the flame and the ground completes the circuit back to the board. If it doesn’t read approximately 5 milliamperes back to the board it assumes there is no flame and shuts off. It sounds like there is something that isn’t quite making and finally gives up. Common problems are a dirty sensor, faulty board and bad ground. Unless the flame rod is physically damaged it almost never needs replacing. A resistance test should show 0 ohms. Usually the circuit board is bad but I have had issues with the house ground where more than 2 volts were leaking into the ground. This takes a good repair electrician to track this down. If the ground checks out good then by process of elimination I would assume it is the circuit board. The problem with your scenario is that it takes a long time to happen so it may take a while to find.