The official Product LifeCycle states that WHS 2011 will be end of life following patch Tuesday of April 2016. However, I'm running into a lot of people who're claiming that it's going to get 5 or 10 more years of patches.
The support until 2020 claims are based on WHS 2011 getting Windows Server 2008 R2 patches; and that OS remaining in support until 2020. This one I find at least somewhat plausible; but "maybe they won't stop" isn't a strong enough claim to defer my current plans to have a replacement NAS operational by early next year.
The ones arguing 2025 are basing it on the first version of the FAQ for Windows Server Essentials 2012 claiming that WHS 2011 would be available as an OEM embedded product until 2025. I find this one completely improbable and that the statement was in error both because it would be 5 years beyond the underlying OS going out of support, and because the FAQ they're citing has been updated to say:
Q: How long will customers be able to purchase Windows Home Server 2011?
A: Windows Home Server 2011 will remain available in all current channels until December 31, 2013. Additionally, under the standard Microsoft embedded OS licensing terms, select OEM partners may choose to continue offering WHS 2011-based appliances for an extended period of time.
I'm hoping to find some sort of official guidance from MS one way or the other; but other than a few "What I'm replacing my WHS with" blog posts on MSDN I can't find anything from the last year or two on a Microsoft domain.