I am encountering the same issue. Grommunio Appliance. New emails don't show up in Outlook 2019 and 2016 (tested both). One has to select another folder in the mailbox hierarchy and then go back to the Inbox to get new messages.
Pressing send/receive does not help. If i delete an email or read an email from my phone, I can see the changes in Outlook but no new emails show up until i change folders. Either that or re-start the Gromox-HTTP service. Once i restart Grommox HTTP, i get shown the mails that were pending to receive in outlook. Then the system goes back to not showing new emails.