You should always download the latest antivirus definitions after a re-build, and keep the system continuously up-to-date for as long as you have Internet access thereafter. Otherwise, you almost may as well not have antivirus protection at all.
That being said, I do not know where Avira stores a copy of the definitions that would be useful for backup purposes, but most antivirus vendors do allow manual download of update files from their website. These should serve just as well as a locally-copied backup, although you will have to download them regularly if you want your backup to stay up-to-date.
A quick Google search turned up this: http://www.avira.com/en/support-vdf-update-info
Regardless, I still strongly suggest that you allow your antivirus application to handle its own updating after a rebuild and thereafter. Only use manual updates for when your system is air-gapped from the Internet, or if it has trouble with an automatic update.