To increase the timeout the following Configuration Setting can be used to modify the default behaviour and allow the processing to continue.
Open the Archive Manager Configuration Console.
Click Advanced Settings
Then add the following Config Property
Exchange Store Manager Worker Timeout Sec
Click OK then
Set the value to 14400
This will increase the time out for the ESM to 4 hours.
Once it gets through the mailbox/s in question then set this config key back to the default of 1800 which is 30 minutes.