I am not an Apple person but the usual answer to this is your iPhone is hogging all the connections. If you have an iPhone, if you turn it off do things go back to normal?

I don"t have an Iphone or a smart phone. I have a normal cell phone with no data plan.

Ok, IMAP server almost universally allow multiple connections. Thunderbird as you would have observed uses 5 if they are available. As Airmail suggested, iphones just use more and more until they exhaust the available connections. There is no set maximum option.

However there are other things that can consume connections and some may surprise you.

Anti spam tools such as mail washer Anti virus programs in their anti spam or anti phishing roles Web mail. The wife sharing the same account on her laptop.

That is from the top of my head. So could any of those apply.

I don't have anti spam tools that I know of. And I don't have anti virus software since this is a Mac. I live alone so no one shares my account. I also have a laptop running Windows 8.1, but I don't have both computers on at the same time. Should I change the connection number back to 5?

do you explicitly shut down the lap top or just close the lid? 8.1 does not shut down but continues running unless you explicitly turn the laptop off.

'I shut my laptop off and unplug it every day. I only use it for maybe about 2 hrs. every night.