Timing is set by the flywheel key.... aligns the magnets with the crankshaft etc. Unless the key is sheared, the engine is in time. If out of time, the engine would not run at all.
However, it's possible you have the points out of adjustment. Reset as follows:
(Point Setting Of Magneto Models)
(J. Reeves)
Set the points as follows. Have the flywheel key aligned with the fiber rubbing portion of the ignition points. Adjust the gap so that a .020 gauge will pass thru but a .022 will not. Should there be any question of the points being dirty (touching the contact with your finger would cause them to be dirty), clean them with a small brush and acetone or lacquer thinner.
NOTE 1: Should the operating cam have a small portion on it with the word "SET" imprinted, align this portion with the fiber rubbing portion instead of the flywheel key.
NOTE 2: Should the cam have the word TOP imbossed on the top of it, that is a cam that could be installed upside down and this is simply telling you which side is up. It is not a position where one would set the points.
You say the engine runs at full throttle awhile then stops..... assuming you still have spark and I'm sure you do as the engine starts back up..... BUT before you attempted to restart, did you pump the fuel primer bulb back up hard? If so, you refilled the carburetor before attempting the restart which would indicate the engine is running out of fuel.
Does pumping the fuel primer bulb constantly, acting as a manual fuel pump make a difference of any kind? If this pumping action cures the problem, that indicates either a failing fuel pump or a bad leakage between the fuel pump and the fuel supply.