Yes CDI's weaken they are basically a circuit board and are affected by heat and internal connection loss. It is quite common to have one work fine for a short time and then fail only to cool off in minutes and work again for a short time repetitively until failing completely.
If it runs at half choke it is probably flooding itself. I would suspect the CDI is weakening or has a bad ground if it runs for a few minutes and stalls out when the ignition demands a faster spark cycle.
Check your vacuum vent on your tank to make sure it is open and check the fuel filter. Some of the outboards have a small screen fuel filter integrated with the line connecter at the carb and some tanks also.
It could possibly be the float level in the carb or a bad needle valve .
You can check the coils with an OHM meter with the same procedure you use for small engines . You can find many how to videos on U Tube that explain it.
Check your fuel line for an obstruction and the primer bulb for fuel flow. Some times on an old hose the inner lining breaks down and collapses when the suction of the fuel pump gets higher with increased speed