Mail app never syncs automatically Despite setting a sync schedule for my my account in the mail app, it has never performed a sync automatically.  New mail is only ever fetched when I open the app, and pull down to refresh.  When I open the app, the "Last synced" note also shows the time I last synced it myself, which might be a whole day ago.

Using the stock mail app on a Galaxy A5 2017, though this also happened on my Galaxy S6.

The account is using IMAP.  I've tried deleting and re-adding the account and it doesn't help.
What version of your Android.? 
Marshmallow? Then my suspect is doze mode are intercept everything when screen off in favour to save some juice (battery) to last little longer.