German
I had a rough idle problem with my bike since I got it. So that's 11 months, 12k miles ago. At each service (Mill) I was told it was a "feature" and that it would be cured when they "upgraded the software" on the bike. After each service the fault was still there. I wasn't happy with the response...then the bike finally failed (again) and was recovered back to the dealer. I opted for a different dealer (Motorrad Central) this time. They checked the bike and said the fault was a “failure of the BMSK controller”. When they went to balance the bike they found the “throttle body butterfly” was also faulty and they had to order a new one. I was also told by this dealer that the idling problems – for the last 12k miles and 3 services – were also probably caused by this fault. I've had the repaired bike back for 3 weeks now, and covered 2k miles. I have to say there is now NO idle problem and it is running sweeter than it ever has.
These are complex beasties...so whilst the symptoms may be the same as your bike, it doesn't mean the cause is the same. But at least it is something you could suggest they look at. The bottom line is German, my bike now does NOT have an idle problem, so neither should yours.