Players have, for the most part, provided excellent documentation to Blizzard concerning the stability. They have done so in a massive thread over on the Customer Service Forums, and it is actively being monitored and commented on by Syndri, a Blizzard representative. The thread was started on March 31st, with the issues appearing a couple weeks before that, and is still active today.
The analysis: There is a lot of Blizzard hate going around about this issue. We've received numerous emails on the subject, and taking a look around the internet and the official forums show the same feelings. This is, in my opinion, unfounded.
Blizzard has came out and said that they know the issue is happening, that they're looking into it, isolating it, and attempting to fix it. They're well aware that people are having issues playing the game – and they want to fix that. It's in their best interest as a business, and as good people (the folks working there are good people, remember). However the acknowledgement by Blizzard doesn't seem to stop a horde of people from saying they're being ignored: they're not. Syndri even makes an appeal to the masses: "By all means, vent your concerns and experiences herein; that's what this thread is here for. But don't-and I do ask this sincerely-ignore the attention that this matter has truly received."