It sounds like an ignition problem to me. If you bike is an oldie with mechanical points, clean and adjust them first as well as change plugs. If a later model with electronic ignition, I'd clean or change the plugs first. Keep in mind that with weak ignitions, plugs can look good but still miss. If that doesn't help, I'd check the resistance of the plug wires. I personally don't like to see them much over 10-12k ohms. If you have resistor caps, be sure to check them too. If everything checks out so far, then it may be the ignition coil. Not sure of the type of coil on yours, but if it has a plastic case, you might look for cracks. That's usually a sign of internal problems. Oil leaking from liquid filled coils is also a problem, although those usually make for hard starting. If all the obvious things check out ok, then you might go through the wiring connections checking for corroded or loose connections, bad grounds, etc. Normally one would think the missing at +3,000 rpms is a sign of insufficient spark strength, but it could be the result of increasing engine vibration acting upon loose connections.
One last thing, many years ago my buddy's '82 FLH kept kicking out the circuit breaker. I finally found the problem inside the headlight shell. I forget the exact details, but there was a wire that had worn through the insulation by rubbing on a bolt, maybe the one that held the shell or direction light on? From the factory the wire was way to close to the metal object and over the years, vibration had done its work. As a precautionary, I fixed the one on the opposite side before it went bad as well.