I'm on a 2012 Macbook Pro running El Capitan. I don't want to upgrade the OS because I will lose some software that I use daily. Everything had been working fine until about 3 weeks ago, then I started having connectivity issues with my mail as follows. I use Gmail for the bulk of my mail, channeled down using IMAP into Mail. I also have my website mail. There is apparently also iCloud mail connected to an email I didn't set up.
a) My website mail continually says it has "an account error" and can't connect. But it does download and send mail. All of those accounts have the little triangle warning beside them that come and go allowing some to say they are offline and others online, even though they all come and go from the same server. I was on with the webmail support, three times, often for over an hour, but despite their efforts, it was not resolved. The problem is not with the mail settings.
b) When I try to send mail, it will often go right away, then other times, it will sit there and pop up that it can't send. If I hit try again, it will often go.
c) Our ISP came out to the house, replaced our modem (twice) and told us all was okay. But that didn't resolve the issues. I also cannot connect with my ftp software. It times out, I believe it's also some kind of connectivity issue.
d) My mail always says it's sending messages, even if the outbox is empty. I know Gmail is often transferring messages back and forth, but it often says they are large, like 4-5MB even if I'm not sending attachments.
e) I have restarted. I have started in safe mode. I have run the hardware check (no issues, it says).
I'm so frustrated. I just want my mail to work.