Since upgrading to sp4 on Backup Exec 2012 I am seeing this error on a couple servers pretty frequently. Before sp4 I was not seeing this error.
 05/13/14 15:45:01 Adamm Mover Error: DeviceIo: ndmpSendRequest->connection error to 192.168.3.70:10000, 10054
Check Windows Events for System Errors:
Event ID's 5,7,9,11,15 These errors point to hardware errors:
Event ID 5. This error indicates SCSI parity errors. This error can be caused by a faulty SCSI card or a faulty SCSI termination. for this error contact the hardware's manufacturer.
Event ID 7. This error indicates that bad blocks exist and can be caused by an outdated tape device driver, faulty media, or dirty read/write heads on the tape drive. Try updating to the most recent Backup Exec tape device drivers, run a cleaning job, and replace the media with new media, if possible. If the error continues, contact the hardware vendor.
Event ID 9. Points to SCSI bus timeouts. To correct this, slow down the SCSI bus and install the most recent SCSI drivers and firmware. & sometimes this error is caused when another device shares the same cable. Try moving the SCSI card to a different PCI slot that does not share the same bus as a RAID controller.
Event ID 11. controller errors, to correct this error, slow down the SCSI bus and install the most recent SCSI drivers and firmware.
Event ID 15. Possibly occurring if the incorrect drivers are loaded or the drivers are not up to date
also you can refer to this TN for troubleshooting help http://www.symantec.com/docs/TECH24414
Are you backing up to tape or disk? If it is to tape try a full power cycle by
1) shutdown both the media server and the tape drive.
2) power up the tape drive.
3) power up the media server
4) check that the tape drive is functioning correctly in the Windows Device Manager and has a Symantec driver.