Based on my experiences, and a slew of other folks posting over at the Blizzard Customer Service Forums, it appears many Tier 6 instances are having issues with stability tonight. Half the raid or more is constantly disconnecting at seemingly random points.
CMs GMs are looking into the issue – but it is wide spread. This means that it is almost assuredly an issue with the Blizzard servers. Based on testing I've done it is not an issue with addons. After a disconnect, all addons were turned off, and the disconnects still happened.
Stay tuned to HKO Insider for the latest. Hopefully they'll hotfix this one right up.
Updated 11:00 p.m. EDT: Belfaire posted "We're gathering the appropriate info now. I have no ETA on a resolution, only that it'll be [fixed] ASAP." (April Fool's text removed for readability.)
Updated 12:44 a.m. EDT: Belfaire also let us know that Q.A. is working on the problem, though no fix has been announced yet. Seems they are at work on it.
Updated 1:00 a.m. EDT: Potential solution from Belfaire: "Please have your entire raid delete or rename your Interface folder and let me know here if you encounter the issue again. [One] group said that they ran without mods, but if what I think's happening is actually happening, even if one person has [an addon], it can affect the raid."