It is certainly possible if the difference in chemical shifts between diastereomers is small. In this case you may try the NMR instrument with higher working frequency, or perhaps use some sort of shift reagent (a rather old technique, but still works). Alternatively, I also suggest to measure 13C NMR - it usually gives a better difference in chemical shifts for diastereomers.

The lack of separation in TLC is not surprising, but for LC-MS, it is - unless your retention time is very short. You may try to modify the HPLC conditions to increase the retention time, this often improve the resolution for the close eluting peaks, or try different type of column. Sometimes columns with chiral stationary phase are very useful in situation like this (yes, it is NOT absolutely necessary for the separation of diastereomers, but may be very helpful).

Finally, if you isolated your material via crystallization, you might accidentally got a single diastereomer, that could be yet another explanation ...

What's your product? If you get an enamine, you will lose one center of chirality and there will no longer be diastereomers.