I don't think so. I had the 24-120 on her when the shutter failed completely, so I wasn't shooting birds. I use the CH/CL on my D7100 a lot more and never gave me problems.
That's not to say that I never use CH/CL on the D750. I normally do short bursts of 3-4 shots.
Wow. That is surprising as I wondered if high speed continuous had anything to do with it. Thanks for the info.