The 'flange recall' may be the cause.
It's a manufacturing defect, not a design issue. HD was able to accurately trace the lot and knows exactly which bikes have the problem. Have them run your VIN #.
A moderatly easy way to check is to shine a flashlight (do not use a match) into the tank when the bike is running. Do this with the tank ~1/2 full. If you see spray or mist, it's probably gotcha. Bubbles coming up from the bottom are normal. Your dealer should be able to perform a fuel pressure test for a more quantitative analysis.
If that's not it...
Mine displayed this behavior when the plugs were getting icky. If I babied it (like in traffic) it would get crabby and sometimes stall. It still ran seemingly fine until finally one plug fouled out bringing it to a head. When considering past behavior things fell into place.
Might help, might not, worth a shot anyway, certinly won't do any harm and plugs are inexpensive.
Factory uses a re-branded Champion plug - most folks in the know won't even run a Champion in their lawnmowers. Replace with
NGK
There are a variety of multi electrode type plugs on the market if you should choose to go down this route. Form & Fit the Gixxer runs the same plug, for function (heatrange) get some assistance selecting something appropriate.
The rear one is easy, front one is a bit of a pain though. Battery & airbox base have to be removed to access it. No special tools are needed.