How to Make Gmail Remember my User ID and Passwords with Safari
There are three solutions I've found. The first two are the easiest and least intrusive, the third one should be tried last as it will remove all saved passwords for other websites too (but the third seems to have worked the most times for other people)

a. Safari Preferences


  Locate and delete the entry for Gmail that is set to 'Passwords
  Never Saved':
  
  


b. Remove Keychain Entry


  open Keychain Access (in Utilities), then look in the login keychain
  and find the site you tried to visit. Somewhere in the list, you'll
  see an entry like this:

www.somesite.com (Passwords not saved)

  
  Simply delete that item from the login keychain, restart Safari, and
  Safari will prompt you to save usernames and passwords when logging in
  to that site. The easiest way to find it in Keychain Access is to
  search for it using part of the website's URL as your search term.


c. Reset Safari


  
  Open Safari
  Click Safari > Reset safari
  Tick Remove saved names &amp; passwords
  Click Reset Safari
  Quit, Repoen and load Gmail