Moving mailboxes in Exchange is relatively a painless task, but when you run into issues like space or network problems then all the moves you started all begin to fail.
Here is an example of a DAG going down and all the moves failing with the following error:
Error: Move for mailbox ‘mailbox1’ is stalled because DataMoveReplicationConstraint is not satisfied for the database ‘DAG1-STORE1’ (agent MailboxDatabaseReplication). Failure Reason: Database <> does not satisfy constraint SecondCopy. Throttling completion as database copies are falling behind.
If you look at the properties of the mailbox move:
and then head over to the details tab:
The solution to this? Make sure the DAG is online and network connectivity restored, you can then resume the move and it should complete.
Hope it helps.