I had a similar problem a while back, but it was the pitch bend wheel that was going funny for me - same sort of thing, ie it was ok if I didn't use it after selecting a patch, but as soon as I moved the wheel it was effectively stuck on. What I found was that it was related to another problem I was having at the same time but had been working around - this was that the 4 control knobs/pots were not able to control the full range of values (settings would only go from say -120 -> 115, instead of -128 -> 127) - might be worth checking if yours are doing the same??
The solution I found was to take my R3 apart, remove the small board on which the control pots are mounted and give them all a really good clean out with a decent contact cleaner. This fixed both problems. I recall other people on here having similar sorts of issues before, where cleaning the pots seemed to help (I think in the end I'll probably have to replace them tho

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I suspect that there is some sort of poorly designed grounding in the R3 such that if the control pots are not working properly then they somehow feed back into the pitch/mod wheels and cause them to go wrong too. Don't know if this is any use to you - and if you're not confident in taking stuff apart then the best thing would be to send it to a service centre - particularly if you're still in warranty.