Updated: (7.30.2018)
Applies to: Add2Exchange Enterprise, Add2Exchange 365 

Even the best of technologies can at times be troublesome.
Known Issues: 

Console Load Error and/or Run-time error ‘429’: ActiveX component can’t create object
http://support.diditbetter.com/kb/a2e_168.aspx - Resolved issue, upgrade to latest

Note:  The above error is not directly related to a sync stopping issue, but only to opening up the Console. 
TIP: If Add2Exchange is stopping, and you have Outlook installed on the replication server to sync to Exchange 2013, 2016 or Office 365, it is most likely you are logging off as the service account,  so don’t. It still runs as a service, but recent MS updates made the system unable to log off.  Keep the service account logged in and lock the machine with that user on and you should be fine. If rebooting though, have to log in and stop and start the Service and then lock as that user. 

During Sync:

Add2Agent Process Exception.: Conversion from string "FTPSite" to type 'Double' is not valid.
Update to latest using normal procedure

Must read to avoid long sync times:  Best practices on syncing calendar appointments and contacts / Disable Social Connector and iCloud Sync

The following is a historical listing of other issues and other relevant information.

There are a few known incompatibilities we have found. We are working hard to fix these, but in the interim these links should prove helpful:

Microsoft Warning about third party devices:

Known issues in underlying infrastructure - Microsoft reported issues syncing Active Sync from earlier Apple and Android devices: https://support.microsoft.com/en-us/kb/2563324
Important Read: http://www.networkworld.com/article/2226464/microsoft-subnet/microsoft-exchange-calendaring-problems---a-current-perspective--mar-2014-.html
LINK: Update to the latest Critical Service Packs on all mobile devices, OWA and Outlook for client machines.

Use this link for workstations: http://update.microsoft.com/microsoftupdate/v6/vistadefault.aspx?ln=en-US

Calendaring Issues solved by Microsoft Critical updates: Microsoft Office Updates and Release Notes

Incorrect Time Zone Settings can cause issues: Time Shift in Calendar Full mesh (bidirectional) if one of the users Timezone is incorrect

Migration Wiz and Skykick Issues when migrating to O365

- 3/17/2017 update - Applicable for any folder type and for many to one or full mesh Contacts Relationship sync.  Some New features will match existing Contact items stripped of named properties.  However, this is only possible for one to one relationships.  Submit a support request for us to do a "preflight" for your ideal Migration plan!

https://www.migrationwiz.com/ 
3/15/16 Named properties and custom fields are not migrated with Migration Wiz or Skykick migration tools- It is critical to upgrade to Add2Exchange Enterprise and sync once prior to using this tool to migrate to Office 365 or hosted Exchange.  Our recommended option is to  dereplicate prior to the use of the tool for migration.  If dereplication is not done prior, the A2O Toolkit is required to remove Add2Exchange Copies in the destination folders.  It has been updated to accommodate the fact that Migration Wiz or Skykick does not sync named properties, the keys we use to determine our copies from originals. Use this link for further information. 

We were told this mailbox migration utility service WILL have functionality for an inplace migration of named properties, at the end of April 2013, yet does not have it as of March 2018. Be very careful when using these tools.

Presently, they are not compatible because they do not copy over the "named properties" of the copied items, so we completely lose control of them.  A local to hosted migration with this tool is not possible without dereplicating Calendars, Notes, Tasks,  Notes and depending on your configuration, Contact relationships. 
Export the setup in the Add2Exchange Console (Help Export Setup) and save it offline to make note of the current relationships, dereplicate prior and then install and license Add2Exchange Enterprise O365,  and set them up again using this new sync technology after the migration.   If Add2Exchange is installed on a Hub or Exchange Server, you will need to move it off to a virgin machine.   If you have migrated using this technology or premigrated and did not dereplicate prior, please contact technical support for the migration assistance immediately before you finalize the migration. 

With a proper onboarding process to O365, it is possible to dereplicate the appropriate relationships and keep some if not all Contact data in place, thereby not losing the Outlook type ahead of those users.   Please schedule a preflight BEFORE migration or presync of related folders.

Google sync

If you are using Google sync, and have bidirectional relationships, this second sync could cause items to revert back to original date or edit.  It is best practices not to have this service turned off.

iOS6 

http://blogs.technet.com/b/exchange/archive/2012/10/23/ios6-devices-erroneously-take-ownership-of-meetings.aspx

*update* iOS update 6.0.1 is now out and most of the bugs have been fixed.  You can read about it here: http://updates.gizmodo.com/post/34769325331/ios-update-6-0-1-is-out-and-its-mostly-bug

ProLaw works with proper configuration

http://support.diditbetter.com/Forums/Thread.aspx?pageid=1&mid=2&ItemID=3&thread=52&postid=114

Windows 2008R2 - Update 3/20/2017 this is applicable anymore

http://support.diditbetter.com/Forums/Thread.aspx?pageid=1&mid=2&ItemID=1&thread=113&postid=225

Microsoft Live Search Maps

http://support.diditbetter.com/kb/a2e_182.aspx

Exchange 2007 and CDO

http://support.diditbetter.com/kb/a2e_193.aspx

Samsung Galaxy III

http://community.office365.com/en-us/forums/158/t/22409.aspx

http://android.stackexchange.com/questions/25232/how-can-i-get-exchange-email-subfolders-on-my-samsung-galaxy-s3

iPhone

http://hosting.intermedia.net/support/kb/default.asp?id=1794

BlackBerry

http://supportforums.blackberry.com/t5/BlackBerry-Pearl/Sync-inbox-and-subfolders/td-p/1408361
http://supportforums.blackberry.com/t5/BlackBerry-Enterprise-Service-10/Outlook-contact-subfolders-are-not-synchronised-anymore-since/td-p/557114
http://blog.link2exchange.com/syncing-outlook-email-folders-and-inbox-subfolders-to-your-blackberry/

Android

http://community.office365.com/en-us/forums/158/t/22769.aspx
http://code.google.com/p/android/issues/detail?id=8072

Changed Items are Reverting Back

It could be that the relationships are not set to copy changes back, so make the relationships to sync back to the source and always overwrite the source with those changes,

It may also be cause by a third party product updating the items.  Please refer to the links provided below as they may help to solve this problem.

Android: http://www.companionlink.com/support/kb/How_to_turn_off_Google_Sync_on_an_Android_device

NitroDesk TouchDown: https://groups.google.com/forum/?fromgroups=#!topic/nitrodesk/GyAvBQ9pzRk

iCloud: http://forums.macrumors.com/showthread.php?t=1245236
https://discussions.apple.com/thread/3380162?start=30&tstart=0