As the mining difficulty gets higher and higher, would it be possible a very high difficulty is unsolvable within the nonce search space?
This is already true now, and has been true for a while. This is why miners modify additional parts of the block header to continue mining.
I am concerned that if it is possible for a high difficulty to put the whole bitcoin network into an unsolvable infinite loop and the network locks up.
This will not happen.
Do we already have some mechanism to prevent this from happening? Thanks.
Yes.