Built three from the ground up. Currently ride an '06 along with two buddies on '08s. At least 5 other local guys I don't chill with regularly ride em'.

There is an issue with the fuel filter getting clogged up. It's a puck type that you have to remove the gas tank to get to. Take it out and clean it good. Some people bypass this and install an inline filter.

At the injector there is also a small screen filter that may get dirty and cause issues. I don't remember how to get to it off the top of my head but some google-fu will getcha there.

If you're experiencing it cutting out when you jump or wheelie, climb steep hills you might get confused at what you're feeling. It could be a fuel delivery issue or it could also be the tip over sensor which has a tendency to shit itself. You can open it up and glue the weight in place or buy one of those aftermarket things to disable it.

If it just ain't running right in general i'd check the fuel filter first as that is usually the cause.

Other stuff to know:

'06 had a recall to address the swingarm pivot on the frame from cracking and eventually failing. You can tell if the recall was performed if it was welded on.

All LTR's have an issue with the shift pin breaking and potentially damaging the case. We're talking $500+ in parts. You want to install a shift pin relocation bracket so the stress is taken off the case to prevent this from happening.

'07 LTRs have a weaker trans than the '06, can't remember what the differences were though so that's gonna be something to google up as well.

'08 has an entirely new transmission and is known for blowing out 3rd gear. Don't know if this applies to '09s as well.

'09 got a badass aluminum subframe.