There has been a problem with always-up-to-date email synchronization for years on SFOS and across many releases, especially if the email account is Exchange and not IMAP. It works at the start, or after a reboot, but then for some inexplicable reason the background sync process just appears to stop and you won’t get any further email unless it is either restarted or you force a manual sync (which rather defeats the object of it).
I believe Jolla made some changes to help improve the Exchange sync in 4.4, but I got so fed up with it for so long I changed to IMAP and set a period sync of 5 minutes. That’s worked reliably ever since.