Took my 2001 Dyna lower rider for a 30 mile ride on the interstate today. Had the throttle at 3/4 for 15 min straight.
Ran real good until I decelerated to exit the hi way, it started missing and sputtering pretty bad when I tried to give it throttle.
I drove it another 5 miles on the side streets going 30 -40 mph and it almost got worse !
I left it sit for a couple hours and it seems to be OK now, this is not the 1st time I went through this.
Any ideas
THX

 

Bad fuel, dirty carb/fuel filter. Loose or dirty battery and ground connections. Check the spark plugs.
Just a few things to look at.

 

I will for sure check those things, the only curious thing is that it only does it on long open runs.
I just drove it stop and go for 25 mins or so and not a hicup

 

Higher speeds need more fuel... check your fuel filter.. but also check you battery connections.

 

It was the loose battery ground that got me. Very similar to what you describe.