An ignition coil that loses its oomph as it heats will give EXACTLY those symptoms. This is fairly common. Have you checked the spark just after it quits running? It should jump 3/8" with a bright blue intense "SNAP".
The clogged fuel filter
issue mentioned by mintyspilot came to mind as well. That can cause fuel starvation that will then self correct over time after shut-down as the fuel seeps through the filter into the system allowing it to run again, for awhile, until the vacuum again over-powers the fuel pump
. But your bulb pumped up hard does not support a clogged filter on the tank end of the bulb.
Debris in the lower end of the carb (bowl, float, needle valve, main jet and emulsion tube) can have this same effect, though the consistant timing of the problem you mention, with the gradually reducing speed, indicates maybe more like a normal-heating-caused issue, like a faulty coil, or an over-heating-caused issue, like vapor lock.
can occur even if its peeing properly - thermostat can fail, blockage due to accumulated salts and mineral deposits can clog certain critical cooling passages, as can debris from a rotten imepller that was not changed in time.
your carb with a kit if its not been done in years. Cheap
The new 10% ethanol in gas has cost boat owners literally tens of millions of dollars in fuel system problems since it was mandated - an outboard mechanic
I know sez his business has doubled since ethanol, all carb rebuilds. When you shut down the engine
for weeks or months, disconnect the fuel line while running at a high idle and allow the engine
to burn the fuel from the carb so it doesn't leave so much 'varnish', particles and crud in your carb as it dries over time.
Marineengine dot com has great outboard engine forums
with many extremely knowledgeable folks that seem to live to help you with those engines... They will work you through the problem one step at a time.
That engine you have is pretty easy to work on once you dig in and go for it. You need to do the carb and check/replace the impeller every few years to keep reliability
up anyway - I'd start with those of its not been done in three years.