Almost sounds like idle/air circuit dirty or plugged. Have you tried any cleaners like Seafoam or Techron thru it?
What type of fuel do you use and is it old from sitting long periods. Any ethanol is bad when sitting in modern day fuel injected engines.
Update!
On the right track from; (bike didn't run for at least 4 years bought whit 1000 klm)
Thursday, 1) Checked the condition of plugs , one was kind of darker than the other one, so new plugs installed, 'just in cases"
2) Then, Seafoam spray injected at 2000 rpm, also (eng.off , idle, few rev up ) and repeat, "took a while to get the right spot to direct properly the spray in the air box hole before i got a engine reaction" Used 1/3 of the spray can,,
After engine cool off, restart idle 20 min no throttle.
3) I added near 1/2 of small bottle, gas conditioner injector & conduit cleaner in full tank ,
Friday, Time for ride, used one tank 250 klm , highway, country, town,
I noticed a change, the eng. smoother,at idle & rpm steady.,
Maybe early, so far; no eng. dying and what i thought normal before ; on quick stop, (engine off) on restart the engine was gaining a 250 rpm, and settle after a while,, i stoped,4 times , eng off, rpm 1050 steady ,
I'll keep doing the process 2 more times using gas "super"
* Also, a previous problem, since i purchased it last year whit 1000 klm , it was bucking bad at slow rpm,"traffic" ( because of low millage & reading to wait until at least 5000klm) before altering or changing anything, suspension or engine).
Now wondering if ? Thanks