These are always fun....or should I say very frustrating.
Since it runs ok for 20 minutes or so...it is not a compression problem.
It is either no spark or no fuel.
Let's try the easiest first....you probably did...but I have to ask...did you try squeezing the fuel bulb until is was hard? Sometimes if one of the check valves are bad the fuel and be syphoned back out of the motor into the tank.
Second...can you tell if you have spark? When you are hanging out of the water it is a very hard thing to do. If you have a timing light, you can put it on one of the plug wires. If the timing light does not flash, then you have no spark.
If no spark, there are only 6 components that make the spark. The exciter coil (under the flywheel), flywheel magnets, pulser coil (on the side of the cam pulley), spark coil, CDI unit and spark plugs.
These are all connected via some sort of connector. Check all your connectors. Pull them apart and reseat them. It could just be a bad connection that gets worse when it gets the heat from the motor.
Pay particular attention to the CDI connections. The CDI is located on top of the motor and is a rectangular box a little smaller than a pack of cigarettes. It is just held on with a big rubber band. Pull it off its mounting and when you pull those connectors (there are two going to the CDI), check the cleanliness of the pins in the CDI. Take a needle nose and give each one a very small twist. This will help make the pins contact better.
You did not say if this has just started happening and if it happens all the time.
Also, what happens if you run it longer than the 20 -25 minutes? Will it keep running? Or will it stop on its own? If it stops on its own, then there could be other things going on.
Also, to get more into checking ignition, you will need a voltmeter and someone who knows how to use it...
Sorry for the rambling....
As you can see the sooner you find out if it is spark or fuel, that will eliminate a lot of things you have to check.
Since your signon is engineer, I hope it is electrical. If you do not have a Service Manual, it would be good to get one at some point. For now, you can find a wiring diagram in the back of your owner's manual. If you do not have one, you can download one for free from the Honda Website
http://marine.honda.com/Owners/Manuals/models/BF15
You will need the frame serial number to get the right one.
Mike