A couple of our clients reported recently that their mailbox restore operations failed intermittently while using Data Protection for Exchange or FlashCopy Manager. Looking at their diagnostic trace (specifically the TraceFileExc.trc file), we noticed FCM was getting a MAPI_E_CALL_FAILED error when it tried to communicate with Microsoft Exchange using MAPI. Long story short, it turns out the mailboxes they were trying to restore contained many folders, and FCM exceeded the MAPI limits in Exchange.
FlashCopy Manager uses Exchange MAPI to perform mailbox restore operations, and it may fail if it has exceeded the limits set by Exchange. To check whether this situation applies to you, look in the event log for Event ID 9646. This Microsoft article briefly discusses this problem for Exchange 2003, but it applies to other versions too. This other Microsoft article details the existing limits and how to increase these limits. objtFolder and objtMessage are the limits that you are most likely to hit, but other limits are possible too. The Windows Application event log will specify which limit you need to increase. After increasing these limits, our clients were able to restore these large mailboxes successfully.