What version of the plugin are you using? V1.0.4 has a fix for one scenario of failed login.
I’ve also had reports of Google sending a “was that you” email with a link to allow logging in.
Check if you got one of those.
If all still fails, please create an admin account for me to investigate. I’ll also have to test your Gmail credentials.
For the admin account, please use the email address vinny [at] usestrict [dot] net.