A lot of times when you are busy doing a mailbox move you will see that the transaction logs can actually grow just as big as the size of the Database. So what can happen is you can run out of space on your database drive and the mailbox move will stop.
To work around this issue you can temporarily enable Circular Logging that will keep deleting the transaction logs while the mailbox move in progress.
To achieve this do the following:
1. Open Exchange Management Console – Go to Organisation – Mailbox
2. Select the Mailbox Database you are performing the move on. Right click – Properties
3. Enable Circular Logging
After this please be sure to enable it as the Transaction logs assist in recovery situations.