You can set SOGoEASDebugEnabled = YES

Thanks. I have now more information in the logs. Once the sync stops I have the following messages in the log:

Apr 25 13:25:12 sogod [5805]: [ERROR] <0x0x7f5f7c3f84e0[WOHttpTransaction]> client disconnected during delivery of response for <WORequest[0x0x7f5f7c249d70]: method=POST uri=/SOGo/Microsoft-Server-ActiveSync?User=user@domain.com&DeviceId=FKHO85VQE92FLBRS464NA1MT80&DeviceType=iPhone&Cmd=Ping app=SOGo rqKey=Microsoft-Server-ActiveSync rqPath=(null)> (len=13): the socket was shutdown

It is not clear to me which socket was shutdown.

Furthermore I have many such messages in the log:

Apr 25 13:25:44 sogod [5733]: [WARN] <0x0x7f5f7c47a7d0[WOWatchDogChild]> pid 5803 has been hanging in the same request for 5 minutes
Apr 25 13:25:44 sogod [5733]: [WARN] <0x0x7f5f7c479fd0[WOWatchDogChild]> pid 5795 has been hanging in the same request for 5 minutes

Any hints what I can do no?

The first message means that the client has disconnected before sogo was able to deliver the response. Could be a network disconnect or the client disconnected for some reason.
The seconds just means that the process is busy with polling for changes e.g. for a ping request.

Please describe more on what happens when "ActiveSync stops syncing":
Does the client stop sending requests?
Can you do a manual refresh on the client?

What does SOGoEASDebugEnabled = YES show while the problem occurs?

No updates provided, suspending.

I found now more useful error messages:

Jun 07 12:18:41 sogod [29584]: <0x0x7f28af6abe40[SOGoActiveSyncDispatcher]> Cache cleanup needed for device BB2BF390D7 - user: email@domain.com syncKey: 93542-232666 cache: 93488-232667
Jun 07 12:18:45 sogod [29584]: [ERROR] <0x7f28af6c0750[SOGoCacheGCSObject]:BB2BF390D7+folder91f0510082621652ed4b00001c9a4368> could not insert/update record for record '/BB2BF390D7+folder91f0510082621652ed4b00001c9a4368' in sogo_cache_folder_r_D_email_A_domain_D_com: <MySQL4Exception: 0x7f28ae732cb0> NAME:ExecutionFailed REASON:Got a packet bigger than 'max_allowed_packet' bytes

Does the client stop sending requests?

Yes, in most cases there are no new requests. It seems as if the client is waiting for something.

Can you do a manual refresh on the client?

If I do a "reload" then nothing happens. If I change the settings from "push" to "sync every 15 minutes" or back then it starts to sync again after a minute or two.

What does SOGoEASDebugEnabled = YES show while the problem occurs?

Most of the time it has shown nothing at all. This time I got now for the first time the mentioned error messages.

Set max_allowed_packet in your my.cnf file to a large value. Your cache exceeds the maximum allowed value by MySQL.

After I had set max_allowed_packet to 64MB the error message about max_allowed_packet went away. But the original problem still exists.

Is it normal that max_allowed_packet has to be 64MB or higher? Or is there maybe another bug related to this which is not showing up in the logs yet?

Yesterday I had the same problem again. I realized then that my emails didn't sync for almost one full day. At the same time the calendar and contacts did still sync. Only the emails didn't sync.

Very strange is, that during the night the device started to sync again.

Could it be that there is a cron job running on the server around 1am which cleans something up which then allows the device again to sync?

There's no cronjob for sure.

The problem does not exist anymore since we moved to version 4. So you can close this issue.