How can I turn off / disable iPhone “Cannot Get Mail” errors?

If you travel in and out of spotty service areas, or have many devices on the same WiFi network trying to grab email from a server with IMAP or POP connection limits, you might be one of the lucky folks who gets inundated with popup “Cannot Get Mail” errors every time you open Mail on your iPhone. If you’ve got multiple email accounts setup on your iPhone, these frequent popup warnings can become extremely frustrating.