check and see what exists on the server..
webmail is convenient for that task.
you could also explore the maildir directly.
Once you know if the missing mail is (or is not) on the server, you'll have an idea where to go with this.
Also - on the long shot that you have VERY large mailboxes, with > 10,000 messages in the inbox... I've worked on several servers over the last few weeks where the quantity of messages (not overall size in MB) has caused indexing to timeout... in this case, you could have inconsistencies like you describe.
Some of these questions may be really basic.. but I need a better picture of the environment and the issue.
All clients are imap (corrrect) ?
You are saying that ALL new mail for ALL users only appears in the inbox of iOS devices and you don't see it in the webmail inbox at all? This happens consistently? If I sent a message to you now, you would never see it in webmail?
Assuming above is all true, and we are troubleshooting ALL mail for ALL users.
What if you quit Mavericks mail, then I sent you mail.
Would you see it on iOS and not in webmail?
If thats true, we can take Mavericks out of the picture.
What else has changed?
When did this start?
The IMAP server can log who moves/purges mail and with those entries, you can track it down to an IP or device type. Its tedious, but sometimes required. To have this level of logging, you need to enable the mail_log.
If you want to head down this path:
For 10.6 server, edit
Look for this section
# Support for dynamically loadable plugins. mail_plugins is a space separated
# list of plugins to load.
mail_plugins = quota imap_quota mail_log
Add mail_log per above
And look for this
#mail_log_max_lines_per_sec = 10
Uncomment and change it to
mail_log_max_lines_per_sec = 0
Stop/start mail service
All clients IMAP.
The missing mail is intermittent. We look to be receiving MOST mail, but not all. And the odd missing piece of mail always seems to be on my iPad, and cannot be found anywhere on my Mac (Mavericks) email. Not in the trash and not missorted. It's nowhere. And it now looks to be nowhere on the server - with the webmail showing the same mail missing.
But it's on my iPad.
This looks to have started about Mavericks/IOS7 time.
I tried to enable the mail log but get permissions errors. Even when logged in as root.
Editing the mail config files has to be done carefully and the information it adds to the logs helps but it still takes alot of sluething to track down an issue like this.
To edit the imap config
sudo pico /etc/dovecot/dovecot.conf
edit carefully and track your changes.
if anything unexpected occurs, you will have to revert changes.
Regarding the mail appear in your ipad.. I bet its cached.
To test, remove the account and re-add it on the ipad.
If the mail is gone, then the only reason you saw it on the ipad is because of local ios mail cache... it doesn't update as often as the Mac OS Mail app does.