Account not synching automatically
Several mail service accounts are set in Mail app (macos 10.12.6). All them use IMAP and SMTP, majority of those is enabled. All are set to server connection automatic management, SMTPs and IMAPs. Mail Preferences > General > Check for new messages = manually.
Almost all are syncing with IMAP automatically, used does not need to carry any handling in order to have new message in Mail app. Except for one. That one exceptional is not Google, if to look onto providers web mail access it is also not Google -derivate, looks like provider proprietary. Why all are synching IMAP on themself except this one.
This problem did not occur until upgrade to 10.12 was made (from 10.9). Before upgrade one does not needed to sync the exceptional one manually.
iPhone 6s, iOS 10.3.3