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Check your choke setting. These twins vibrate quite a bit and it could be changing position.
Also, make sure your carburetor is securely bolted to the intake and there are no vacuum leaks developing when the engine warms up.
You can "spritz" (spray) water at the gasket to see if the engine changes pitch to find a leak.
Good luck.
Well, it doesn't sound as if you have a fuel pump problem but the diaphragm is available through boats.net and they do ship world wide.
https://www.boats.net/catalog/honda/outboard-by-hp-serial-range/15hp/bf15ax-las-1999/fuel-pump
Also, the gasket set containing the jet oring is available from the same place. Refer to the related links.
https://www.boats.net/catalog/honda/outboard-by-hp-serial-range/15hp/bf15ax-las-1999/carburetor
Good luck.
The best method to find a vacuum leak is to use propane gas it will tell you almost instantly if there is a vacuum leak.
I agree with Tegwini about using propane to find intake leaks AND to troubleshoot lack of fuel issues.
I suggested water because it also works well too (most times)and most people are not as reluctant to try it. But, yes, I use propane myself pretty much exclusively for finding intake leaks.