We received a tip from a community member who suggested this as a work around for unlocks not saving:
The default mutiplayer screen is bugged and will not save anything you unlock whilst in that screen (Weapons, attachments, mystery dog tags, suit modules).
The only work around i have found and which has worked for many other people is to join a server, preferably an empty one and unlock any equipment etc in that screen.
After you have finished that leave the server so it says "Updating Profile" then exit the game and start it again to double check but all of the unlocks should now be saved.
So, essentially you should try unlocking your items whilst being connected to a server, instead of doing it from the main menu.
Please give this a shot and let us know your results

Thanks!