Email accounts dropping offline/online-sometimes they work, sometimes not.

Question

I have 6 different Gmail accounts set up to be managed via Apple Mail. Recently they're connectivity has been unstable. They will fluctuate from being online and offline. Two of my accounts have gone offline (at they Apple Mail end) completely. This is very disruptive not to mention irritating!
How can this be prevented and how to I reset whatever needs to be reset?

Answer 1

The problem is probably that when Mail checks for new mail, you have too many connections open with the same server at the same time. Some mail servers refuse connection attempts if they are too frequent, or limit the number of simultaneous connections that are allowed from the same IP address.
If that’s the problem, there is little you can do about it. Mail doesn’t let the user configure the maximum number of simultaneous connections.
Do you access any of those accounts some other way (e.g. webmail) while Mail is checking for mail?
What’s the time interval chosen in Mail > Preferences > General > Check for New Mail? If it’s set to Every minute, try changing it to Every 5 minutes.
Just in case this is a network issue rather than a server issue, go to Apple Menu > System Preferences > Network, choose Network Port Configurations from the Show popup menu, and make sure that the configuration used to connect to Internet appears at the top of the list. Leave checked (enabled) only the port configuration needed to connect to Internet and Built-in Ethernet (in that order if not the same), uncheck (disable) the rest of network port configurations and see whether that helps — if it doesn’t, turn ON again the ones you want enabled.