Dave,
You did the right thing...pulling the plug wires. That pretty well eliminates the spark plugs and the coil. Although, I have found with ignition....nothing is a sure thing. You only have four things left... 1. The exciter coil, 2. The pulser coil, 3. The CDI, 4. A connection.
The cheapest thing is to do a wiggle test to all the connections. Also, push and pull and the connectors and wires going in the CDI (the thing little rectangular box on the top of the engine that looks like a pack of cigarettes).
If you know someone with the same vintage Honda 15 (even a 9.9), borrow their CDI and give it a try. It is held on with a big rubber band and has two connectors that just unplug. It could be misfiring.
The only real way to track it down (assuming it is ignition) is to put a voltmeter on the exciter when it is running good to see what it reads. It will probably be around 150v p-p ac. Do the same for the pulser. It is generally 3 - 5v p-p ac. Also, do the same for the inputs to the coil (output from the CDI).
When it fails, measure them again. If there is a change, in any one of them, that should give you a new heading. Just remember... a change in the exciter or pulser output will cause a change in the CDI output. If only the CDI output changes, then it is most likely the CDI.
There is a wiring diagram in the back of your owner's manual. If you do not have yours anymore, you can download one for free from Honda.
Honda Marine - BF15 Owners' Manuals
Mike