An attempt to connect to gmail failed

It looks like you are trying to get mail from server  not gmail  check your account parameters

Could still be a private domain hosted by gmail.  The question is, are you able to send messages successfully?  If yes, it could just be timeout errors and emails are sent on subsequent attempts.  I get these on occasion as well, I just ignore them.  If they bother you, you can turn off notifications by going to menu/tools/settings/general/general and uncheck “Show window when error occurs”.

If you are unable to send at all could be a number of things:

  1.  wrong port (should be 587)
  2.  wrong security policy (should be “Force usage of SSL/TLS”)
  3.  Anti-virus software interfering.