It seems that the problem is to do with either gMail Token or port 465 that isn't (always) working...
The way to solve the problem is the following.
1) Deactivate gMail's eMail in "Mail, Contacts, Calendars" ;
2) "Add Account" > "Other" > "Add Mail Account" using the following :
your@gmail.com Email for address and username ;
a) Receiving : Using IMAP the receiving server is "imap.gmail.com" SSL port 993 ;
b) Sending server is "smtp.gmail.com" SSL port 587 ;
Of course make sure that IMAP is enabled (from gMail webpage under top right gear "Settings" then "Forwarding and POP/IMAP". If you use 2 step verification be sure to generate a specific password for that device.
PS : you could setup the account using "Exchange" and "m.google.com" for server but this is very unofficial.
The real problem from Apple is that they lock changes to the "sending" server if configure using the "userfriendly" "Google" choice under "Add Account". I believe to avoid further problems they should allow user to change the default settings and for friendlyness add a "Reset to defaults" button while manually editing the Google account... This would always enable user to use their Internet provider or company specific mail server instead of Google as the Mail app isn't switching from the primary to any "other SMTP servers"...