The issue maybe is that you have 2 variables Savedate and Lastsavedby when you close the dwg these will probably disappear, so no update,
I have started using this for saving info in a dwg, rather than variables 1-5, Userr1, Useri1, Users1.
(vlax-ldata-put "StevenP" "SAVEDATE" yourdate )
(setq savedate (vlax-ldata-get "StevenP" "SAVEDATE"))