The datetime function supports the Extended Capability of C/C++ Code Generation (with some limitations listed on its documentation page) but save does not support C/C++ Code Generation. Looking at the list of Data Import and Export functions that support C/C++ Code Generation you may be able to write the datetime objects as text to a file using the low-level file I/O functions fopen, fprintf, and fclose.
Alternately you could write a MEX-file that calls into MATLAB to create the datetime array and save them to a MAT-file, but if you're going to do that why not just write a MATLAB function file to do the job?
