I had this problem too.
The problem arises because flightplans are stored within a sub-folder in the FSX main
install directory and FSX doesn't have administrator rights to write files in this
directory. So when you try to save a file by clicking EXEC nothing happens because
PMDG737NGX doesn't have this right either.
Here's the solution:-
1. Find your FSX main install directory.
2. Right-click on FSX.exe
3. Click on compatibility tab and check "RUN AS ADMINISTRATOR"
4. Repeat 4. if sub-windows appear.
5. Restart FSX and Windows should ask whether FSX should be granted administrator access. Click "YES."
Flightplans should now be saved when you click EXEC and appear under CO ROUTE in the FMC.
Hope that helps.
Ian