Mail times out

Recently my Mail frequently malfunctions with the error message: "Connections to the server “p48-imap.mail.me.com” on the default ports timed out." I've seen other similar posts, but no solution. It's happening on both of our iMacs, but not on our iOS devices. Sending and receiving email from the iCloud webpage works fine. I've replaced my cable modem and have very fast internet speeds. This problem is the same with High Sierra and with Mojave on my iMac and with El Capitan on my wife's iMac. Any ideas?