Sounds a little like the problem I just had fixed. First indication was that it was jumping out of gear and then, because I was riding more carefully, it wouldn't engage properly. 2nd and 4th were the worst. Shift lever was 'soft', but not floppy. Was also really hard to find neutral - or rather get the light to come on - which was a real bugger because it wouldn't run or start with the stand down even though it wasn't in gear.
Mine was a broken detent spring. It can be fixed by removing the front cover of the engine, rather than the engine needing to come out, but many guys have reported that dealers pull the engine, costing meg bucks in labour. It should only be about an hour's work if done properly. My sump also had to come off because they couldn't find all the bits. I was lucky because Triumph Australia agreed to do it as a warranty job even though I'm out of warranty (by 3 months).
Take it to your dealer and get them to diagnose the problem. If it's (probably) the detent spring also contact your local Triumph rep to see if they'll come to the party - don't leave it up to the dealer to do that. Tell them you know this to be a common fault that certainly shouldn't happen after just 15000 miles even on an 08 bike and that it should be rectified (as a goodwill gesture if nothing else).
If it's something else wrong with the tranny you should still make the call to Triumph. You never know! Our guy here is Aus is fantastic and very fair. Good luck!
Edit - I know this is the Touring Forum and your bike is a Touring, but I think the problem/fix could be same as for a Standard. Hence my comments above.