If it's a website of a decent size, and it's down, you're certainly not the only one who sees the problem.
See who might be complaining about it on Twitter: http://twitter.com/#search?q=sitename
If you're afraid that the site has closed down without alerting you, again if it's a fairly large site it will be noticed. Try a web search for "<sitename> closed". Change "closed" to "down", "gone", "dead", or equivalents.
Many sites have a blog to alert their user community to news and changes at the site, and they're often hosted elsewhere and/or on a different domain. Do a web search for "<sitename> blog" or "<sitename> news".
Some sites also farm out help and/or community pages. Even if they don't, there are places where users congregate. Check Google Groups and GetSatisfaction.com for information.
If it's not big enough for any of these things, then it may be time to start looking for alternatives.