What code did you get and did the code come from the ECM or the TCM? The TCM gets the engine speed signal via CAN whereas the ECM gets the signal directly from the crank sensor. I don't recall reading of a fail safe (limp) mode based on crank sensor signal but engine speed is listed in list of inputs/outputs to the TCM that can cause a fail safe mode. If you have a bad crank signal detected by the ECM, the car is just going to run like crap or stall because it doesn't know where the pistons are and when to fire. Does the car stutter and run roughly/poorly or does the engine run smoothly but not exceed xxxx RPM? If the engine runs fine and the TCM is detecting a problem with engine speed data, that might trigger some kind of fail safe operation of the CVT even though I don't see one listed.
When I had a bad crank sensor in a G35 (basically same VQ35DE as 1st gen Murano), the car would randomly stutter and run like you're hitting a rev limiter and then just as quickly go back to running 100% perfectly. The randomness increased to more often and for longer bursts of poor running and then back to 100% perfect. Then after about 2-3 weeks of this behavior with no code, the car stalled on the road and wouldn't re-fire no matter how long I cranked it. After letting the car sit for an hour, it re-fired and I drove it home and had a crank sensor code. If this sounds like your car's behavior, I recommend you get a new crank sensor before your car leaves you stranded somewhere.
If your car runs smoothly but doesn't exceed certain throttle percentage or certain RPM or gear ratio (how are you determining it's in 3rd gear?), it doesn't sound like a crank sensor problem to me but who knows..... I haven't had one go bad in my Murano. There's a chapter in the FSM for the CVT that details all the CVT fail safe modes. The CVT chapter does mention that the engine speed sensor (crank pos sensor) is an input to the ECM and this info is communicated to the TCM via CAN so may have some relation to CVT operation but I don't see a specific mention of a fail safe mode that gets triggered if you have a bad engine speed input. There's a fail safe mode for primary speed but I think this is measured in the CVT with a different sensor that really only needs to measure rotational speed rather than the crank sensor which needs to read correct crank angle. Most of the fail safe modes say they disable manual mode so if you have no manual mode, that's an indication you may be in a fail safe mode. The CVT chapter also has lots of details about the various CVT related DTCs so if you have a specific code and it's related to the CVT, that chapter may tell you how to investigate.
Good luck!