I ran into this today, doing my first production DAG with a copy on a kind of slow connection.
Error: Move for mailbox '/o=First Organization/ou=First Administrative Group/cn=Recipients/cn=user' is stalled because DataMoveReplicationConstraint is not satisfied for the database 'Database' (agent MailboxDatabaseReplication). Failure Reason: Database a409ab86-ce24-4fcf-bd2a-14fd633090aa does not satisfy constraint SecondCopy. Some database copies are behind.
Sure enough, a quick check of get-MailboxDatabaseCopyStatus showed that my CopyQueueLength was fairly high on the server across the WAN. As a result, my mailbox moves were failing with the above error. However, they don't fail right away, the StatusDetail shows StalledDueToHA. Some stayed there up to two hours waiting for the log shipping to catch up on the remote server before failing.
To show a more detailed output on move progress, I was using:
Get-MoveRequest Get-MoveRequestStatistics | ft displayname,*stat*,perc*,totalmailboxsize
So what Exchange 2010 is doing here is smart. Exchange Active Manager doesn't want that CopyQueueLength to be over 10 files, or the replay queue length over 50. More constraints here.
The workaround is to disable this limit, so your moves can occur and the seeding can occur over time. This is one of three Microsoft recommended fixes. One is fix your database health, one is upgrade your WAN. This third one is a workaround that should be reconfigured after the initial mailbox moves.
Set-MailboxDatabase -DataMoveReplicationConstraint None
The default here is SecondCopy. More information on the other settings at the link above. This change DOES require a restart of the Exchange Replication Manager service. Be forewarned, if you have a queue length already, the replication manager will hang on stopping and attempt to complete the copies before stopping, so it might take some time.
Of course, once your moves are done, and your database's CopyQueueLength is normalized, you should re-enable this constraint using:
Set-MailboxDatabase -DataMoveReplicationConstraint SecondCopy