I think you could be forgiven with an RT, I tend to remove my tools from what ever they were fiddling with and have a generic "Swarf-come tool pit/ tray" set up infront of me; whose contents could vary in anything from a mic, to a spanner, to nylon swarf to a spring steel pocket ruler and black sharpie. I find it very useful and comforting. I also have a trolley behind me containing my hammers…i always like to have them close to hand. 
Getting back to your Chuck, The RT, is it a front mount chuck on a tee slotted base? or a threaded nose? The latter we can pretty much rule out being the cause in all but the most battered of circumstances.
The front mount is an interesting one because it's difficult to centre, I puzzled myself with how i could set it up til i realised i could turn a dowel to fit the back of the chuck to the RTs MT2 spindle bore, jobs' a goodun.
But i suspect you've already ruled that out, and are pretty sure it's the chuck, I did notice the chinese one has a sharper angle ground on the tooth and they do form a much rougher triangle.
This is strange, because as you say, it was working fine before, I would look at the chucks own scroll and the corresponding jaws scroll, it could be that jaw 2 has worn thin and it might have some noticable slack?
PS. I really doubt it's this also, but it just occured to me that when fitting the jaws, i always look for the bite point when going round the numbers. I slip it in and out as i carefully turn the key and wait for it to just take it. i never turn it beyond the bite point or it could go in a odd order?
normally this is very very obvious, but maybe theres a chuck out there where its very subtle?
Michael W
Edited By Michael Walters on 07/10/2016 18:40:09