Want a tip from me? If you get a notification via Google Webmaster Tools about an increase in server errors, an outage, increase in not found errors, GoogleBot not being able to access your site or any of those types of errors - do not ignore them.
If you know the cause and you know it is temporary, you can ignore them. But if they happen over and over again but you are convinced that nothing is wrong with your server or web site - don't believe yourself.
If you keep getting these errors, something is wrong. Google is having issues accessing your web site and if Google continues to have issues accessing your web site, than Google will not want your web site in their index.
This happened to one webmaster who posted his story at WebmasterWorld.
He explained that he simply ignored all the warnings because his server was fine, at least he thought so and still believes so. But it resulted in his site being almost completely delisted from Google.
Middle of last year, Google suddenly started sending me warning mails via my Webmaster Tools account, telling me about "possible outages" and that "Googlebot can't access the site". I looked into those, and noticed that Google had found (and decided to spider) the default /links directory, even though it isn't actually linked anywhere on my site. Thinking that Google had no business crawling that directory in the first place, I simply ignored those messages.
Obviously, I shouldn't have: Over the course of 5 months and accompanied by a total of 30 warning messages, Google eventually started slamming my site, moving it down from page one to page 80 and beyond.
As a result, the number of my indexed pages dropped from "several thousand" to "several dozen".
If you get these errors (note the image above is photoshop'ed so I don't get those errors) do act on them. Bug your hosting company, ask people around the world to try accessing your site. Use Google's Fetch As Googlebot feature. Test it and test it and make sure the error notifications stop.
If you are unsure, post in Google's Webmaster Help forums.
Forum discussion at WebmasterWorld.