Help! Gmail on mac not working any more

[fasterthanthewind]

This is INFURIATING! (and it's going to be an essay...)
I have a gmail account, which I access from my laptop (via Mac Mail), and via whatever Mail program the iPad has as well.
Has always worked beautifully.
Since Sat, I've been able neither to send nor receive messages from the laptop. Connection is fine (so says connection doctor), but if I dig around enough I eventually get to an error message that says
'Too many simultaneous connections'
So I went into gmail webmail and down to the 'activity' thing at the bottom and asked it to close everything: no change
Changed my password: no change
Turned Mail off for 24 hours; rebooted laptop: no change

What else can I do? Why is this happening?

It isn't a catastrophe, as I can still use webmail and mail on the iPad but it is a nuisance, and I'd like to know what's gone wrong so I can fix it.

Dear Mac-users, please help!

From the apple support website:

Gmail has a limit of ten simultaneous IMAP connections per account, and checking your account from multiple devices in a short period of time can exceed this limit.

support.apple.com/kb/TS2976

Have you been checking your email from two devices more frequently since Saturday?

No I haven't... And there's a place where you can (apparently!) shut down extra connections - tho it says I don't have any anyway.

So I'm FLUMMOXED.

I am wondering if there is any other way to see what is happening and why...

I deleted the account and reinstalled it, and that fixed it. Dunno what happened, it was as if something had 'got stuck'.