Greetings,
I understand that the exhaust runs very close and below the petrol tank and in some instances this can cause the petrol to get quite warm, which intern can cause the impeller inside the pump to expand, which compounds the problem with possible pump failure
Another possible problem might be the small ball in the fuel filler breather which can get stuck and cause a partial vacuum again resulting in petrol starvation. If it is similar to those fitted to Gas Gas then fit an extra length breather pipe and remove the ball.
There is a replaceable filter in both the tank and the inlet of the injector, check out with a KTM dealer who should be able to advise further as I think that the injector filter was modified.
You might look to heat insulate the underside of the tank by fitting a pad such as you will find under Triumph road bike petrol tanks
Check out this video link too;
https://www.youtube.com/watch?v=qFU3JCkIYS8Make sure that you really do recharge the battery, preferably with a charger such as an Optimate 6 model, and leave it on charge for at least 12 hours. I have an additional lead permanently wired into the battery and my bike stays on charge permanently when in the garage.
Hope these ideas help, please let us know how you get on.
TTFN
Hugh.