DOI exists since 1997, which is pretty much since forever in internet time.
Figshare on the other hand, not so much.
Figshare on the other hand, not so much.
http://figshare.com/blog/Ensuring%20persistence%20on%20figsh...
Twelve research universities keep copies of all the data and will make it publicly available should Figshare implode.
Other data repositories, like Dryad, do the same thing, and grant agencies with data deposition requirements usually require you to deposit data somewhere that has a long-term plan to ensure access.
So as long as the twelve universities manage to update all the DOIs to point at the new locations, Figshare DOIs should be reliable.