What is "Paused (On Battery)" mean in Mail.app?
It may have paused while you were operating your MacBook on battery power. As per Apple support document, If Mail on your Mac downloads messages only when you open them:


  When your Mac notebook is running on battery power, Mail in OS X El Capitan conserves energy by pausing the full download of messages that are that are older than 30 days, or older than the 10,000th message downloaded. Mail downloads messages from newest to oldest.