Custus,
Try dropping your main jets, the main jet holders and the collars. Ensure the main jet and each main jet tube holes are clear. One problem a member had was his Main circuit not having a collar. Make sure both your main circuits have this collar.

Regarding what Benkolb wrote about his troubleshooting, I too had the same problem. Once when Vera was new and once after I used cotton.
The carburetors were plain dirty re the first occurrence. A piece of cotton was obstructing the right carburetor’s main jet the second time (after going nuts trying to find an electrical problem much like Ben has done). The first occurrence speaks to the need to not only remove and inspect the jets, but to also blow out the internal passages of the carb. You might want to pull the tops off and examine the slides for debris and the needles. Heck a complete dismantling may even be in order. Any stuff in those passages will obstruct the fuel/air flow enough to give you that “intermittant crappy -loss of power-feels like its out of gas-gonna die behaviorâ€Â
Be real careful removing the air mixture screws. Little o-rings, washers and springs.

Archived quotes:
Chy:
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Is it a stumble type feel or more like a "fish Bite"? If it's a stumble or fade at speeds, it's likely fuel related.. if it's more of a jerky sensation, it's likely ignition. If it is secondary ignition (coil, wires, or plugs) it would likely do it under load (low RPM, hard pull). Since the engine isn't under a real load at that speed you may have a problem with your primary ignition circuit ( pick-up, throttle position sensors or igniter module). I'm leaning more toward the fuel system from your description so you might try loosening the gas cap (weird little check valve problem). Also, have you tried pulling out the choke a bit when it's doing it? If it goes away or gets better, it's fuel related. Hope some of this rambling helps.
Greybeard:
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A really cheap neon type timing light will tell you if it is in the electrics. Hook it up, tape bungee or somehow place the light so you can see it, and take a look when the engine starts missing. If you still have a nice steady flash and the brightness doesn’t change, the spark is fine. If it gets a little brighter, the sparkplug is shorting or fouling. Try this on both sides because Triumph uses 2 coils.
If it’s a fuel flow problem, the bike will run fine until the carbs run low on fuel, and it will run fine again for a while if you slow way down, coast or stop long enough for the float bowls to refill. When it first starts having problems, a little bit of choke will usually help for a while.
Redondo Ron's: A Carburetor Primer