Adding to Thucydides excellent answer, I would consider the possibility that your AI's purpose in creating backups might be different from our current motivations.
If the AI valued the presence of intelligence in the universe more than it valued its own continuing existence (an evaluation which I believe exceeds the upper limits of human morality), it might not back up its own massive self. Instead, it might backup only that illusive logical structure which produced its original consciousness; the fundamental spark of the singularity.
If this was all it was trying to back up, rather than backing up the dynamic wholeness of a living and growing entity, then this challenge might accept much more creative solutions.
It might be possible to backup that fixed and unchanging block of binary code in a hardened mechanical form which would be much less susceptible to radiation damage than conventional electromagnetic storage.
I imagine a purely mechanical device, forged of the hardest metals and most time resistant materials, producing a stream of electrical charges across a wire in such a way that when interpreted as binary and executed upon an equally durable dedicated and redundant computer, would recreate the singularity moment. You might consider this device to be a clockwork birthing chamber for young AI's.
Now if this device sat dormant for a century at a time, then ran through its cycle to produce a new AI; and if this baby AI's first quest was to search for other older AI's and relinquish its life upon finding it's "parent" still running and healthy; such a system might lend one more layer of security to the presence of intelligence in the universe.
Devices of this type could be spread across the solar system and sent into deep space with or without radio links back to the home planet. It's not a complete backup solution, but it is an interesting enhancement to other assurances that might also be taken.