Assuming you're referring to the Svalbard Global Seed Vault, the Wikipedia page answers your question:
> In October 2016, the seed vault experienced an unusually large degree of water intrusion due to higher than average temperatures and heavy rainfall .... The vault was designed for water intrusion and as such the seeds were not at risk.
If things go far enough downhill that the Svalbard vault is lost and its contents just allowed to rot, I’d be surprised if we retained the technological capacity to do things like synthesizing a complex genome from data. (I’m not sure we could do that with present technology either, for that matter.)
Libraries and museums burn down all the time, or get destroyed in wars. Consider the recent fire at the Hewlett-Packard museum, where all the paper history was lost. Nobody made a backup, even though paper lasts longer term than data on a hard drive.
Frankly, I think storing data as ASCII in pits on a substrate is a great long term solution, as it can be read with a simple optical microscope, and ASCII is forever.
One of the cool things about digital data is it can be copied forward limitlessly. Make the seed genomes public domain and put them on a server - people will make copies, like they make copies of wikipedia to store in their prepper bunkers.
Even with the digital copy of the genome, you have to synthesize the entire genome, the cell it belongs in, and the rest of the seed to get a plant. That seems... possible, but hard enough that it doesn't make sense to call the sequenced genome a "backup".
https://en.wikipedia.org/wiki/Gene_bank
e.g.
https://en.wikipedia.org/wiki/Seed_bank