Have a gas forced air furnace. Not sure of the name brand. When it calls for heat, the burner kick on, but won't stay on. They will burn for a short period, then they will turn off. The fan motor stays running, but I had to turn the start temp for the fan way down so it would blow what warm air there is in the unit out. It just keeps repeating the cycle. I put in a new fan limit switch and it does the same thing. My next step I think is to get a new flame sensor. If this does not fix the problem, I don't know what to do after that.

Have you cleaned the flame sensor that you already have?