Dumb question.. How long are seeds able to be preserved without a (reup?)
Germination rates drop over time. Storing seeds improperly will increase that rate (i.e. even fewer seeds will sprout after a give time). You'll more-or-less always get a few to sprout, but you can't count on getting the vast majority to sprout unless you've stored the seeds properly.
If seeds are stored at high temperatures (room temp or above) in non-airtight containers, they typically have a "half-life" (non exact) of a year or two.
If you store the seeds in an airtight container in the freezer, they'll keep more or less indefinitely. (I'm guessing, but let's say a "half-life" of a decade or so.) There are instances of seeds preserved in permafrost sprouting after tens of thousands of years: http://en.wikipedia.org/wiki/Oldest_viable_seed
All of this depends on the type of seed, as well. Take my numbers above with several grains of salt. They're from general experience growing up on a farm, not any definitive source.
In practice you lose more over time so it greatly depends on how many you start with. However, you could encode the DNA in another format which effectively means unlimited shelf life assuming you a reasonably close species to work with.
Tissue culture requires tissue that is alive. The live embryo is removed from the seed and placed on sterile media containing nutrients and hormones. The exact composition varies depend on the plant species / cultivar you are working with.
Tissue culture is useful as a last resort for breaking seed dormancy, but if the problem is that the plant tissue inside the seed has died, it will be no help.
http://en.wikipedia.org/wiki/Human_Interference_Task_Force
about trying to solve how to say "dangerous radiation" so people in distant future would understand. Not trivial task at all.
The real issue is you need to encode a lot of data in a stable form for a long time for cheap enough someone would pay for it. Pluss, the cost of actually sequencing 10K+ plants * a few examples so you have some genetic diversity.
Agree with the poster who states this is a case of bureaucracy gone wild. There are reasons the initial laws exist (insure consumers are buying viable seeds and that are the species represented), but hey... give some people a little power and they start finding ways to use it.
I honestly don't think "big agrobusiness" cares about backyard gardens. But I might be wrong.