Confirmation emails are not received when booking a resource with a migrated room mailbox.
When booking with a natively-created room mailbox, a confirmation email is sent to the person making the booking that says "Your request was accepted". The meeting appointment shows the name of the person booking the resource in the subject.
With a migrated resource mailbox the booking is still made, but no confirmation email is sent. Insead, a pop-up message appears that says "The resources for the meeting were successfully booked". The name of the person booking the resource does not appear in the subject.
This can happen even when the mailbox has been converted to the correct type (refer https://support.quest.com/SUPPORT/index?page=solution&id=SOL46313).
This can occur when the resource mailbox profile is reconfigured manually.
Microsoft detail the steps required in the following article: http://technet.microsoft.com/en-us/library/bb232195.aspx
In particular it should be checked that the "Automatically accept meeting requests and process cancellations" option is cleared before updating the mailbox to the correct resource type using PowerShell.