Unsure if this is a common issue, but it happened to me yesterday and it's a very quick and easy issue to diagnose and repair with a bare minimum of tools and mechanical expertise.
I was riding my R3T at a moderate speed on a San Diego freeway when all of a sudden, my throttle no longer responded. My speed rapidly decreased, my throttle provided no response (it just spun 90 degrees) so I coasted to the side of the road in nuetral.
I figured right away that it was a problem with a throttle cable (either broken or disconnected).
All I had with me, tool-wise, was the stock plastic baggie of Triumph tools. Gulp!
That turned out to be fine, as all that was needed were the phillips and flat-bladed (standard) screwdrivers.
I unscrewed the throttle casing, held together with two phillips screws, and sure enough, one of the two throttle cables was hanging loose.
I pried it out with the end of a standard screwdriver and pushed it back into place with my thumb. I tried the tension by testing the throttle--everything felt fine.
I put the throttle case back together, screwed it back in and was back on the road in about 5 minutes total.
I hope this easy fix helps another Rocket Captain one of these days.