I have a similar problem that started last night. A small email got stuck Sending Message. I deleted it from Outbox, but cannot send any email now, but am still receiving email. When I sent a test email, it got stuck Sending Message. When it is stuck, the message repeatedly flashes on and off the screen; and nothing will stop this behavior except deleting the message from the Outbox. I've tried restarting Mail and restarting computer to no avail. I am running OS X El Capitan 10.11.6 on iMac. I am up to date on updates from Apple. I also cannot send email from iPad, but don't get the flashing behavior. Now I'm trying the Apple Support Community.