New problem

have you check the Spark Plug leads for excessive resistance, this can be done with an ohm meter, you would need to check with an auto electrician the max ohms as I cant remember of hand, you could always check them all and not all will go at the same time but you may find that one or two may have a lot more resistance than the rest. ..... just another thought
 

Just seems like a clogged fuel filter would cause it to run bad all the time and not just after 20 minutes. Also, seems like a clogged fuel filter problem would get worse above 2k instead of better as it starves the flow. Seems like a sensor breaking down as it gets hot.
 

When I read the first post I immediately thought fuel filter and/or trash in the tank. Trash in the tank will slowly get stuck on the filter screen and then restrict flow. Once the bike has came to a stop or the gas gets sloshed around in the tank then the trash falls off the filter. Then the cycle starts over again. However I believe you're right..... it's most likely electrical.
 

I have a good ohm meter. I can check that easy enough.
 

Now it doesn't get worse after riding it. It starts acting up right away.
 
................... seems like a clogged fuel filter problem would get worse above 2k instead of better as it starves the flow....................
Agree with that, had a similar problem on a car - run fine until demand increased. Turned out to be a small filter in the tank that wasn't shown on the parts list.
 
OK, I spent some time on the Rocket today. I removed the gas tank and crimped and tightened the front coil primary wires which I couldn't really access that well previously, checked all plug and electrical connections, cleaned and gapped the plugs (which were off), checked all vacuum hoses, went back to the stock tune (checked O2 sensor box), and tightened the exhaust manifold bolts. I synced the TB's a while ago so I know that's all set. I have cat deletes and I previously removed the secondary butterflies. Finally, I went through all the diagnostics and tests with TuneECU and did the ISCV adjustment and reset adaption. When I did the coil primary wires and gapped and cleaned the plugs, it cleaned it up quite a bit. Going back to the stock tune made it better and lastly checking the O2 box off made it even better. Does that make sense? Anyways here's a video I made today and some screen shots from TuneECU. It's back to being smooth again and even revs pretty quick. Some dyno time with a pro tuner and this bike would wail! Glad I didn't give up on it, it's a great bike.

 
If I even had a thought about it being a clogged filter I would change it quicker then stink on crap!!! I mean what are we talking 7 bucks for a non Triumph filter you can get at a auto store. I am not siure how many miles are on the filter you have but if you got into some ****ski gas it could mess you up. I would also look at what my idle rpms were set at per temperature. as I see in your screen shots I would think 750 is to low especially looking at the safety of oil pressure at them low rpms.
 

I would have done it in a minute if I thought that was it. I was just thinking out loud. Plus it ran fine at high revs so that kind of rules that out. The bike only has a little over 3,000 miles on it.
 
if it has not seen the dealer much there was a idle map recall in 06 for all rockets have you down loaded a recent map into the bike?