They did, but only barely. I recall hearing that shortly before they acquired NEXT that the chief executives were shopping the company around, hoping to get bought out. However no one even wanted to buy them.
Apple of 1985 is very different from the Apple of 2008, however. I would say that Apple is much, much more popular now than it was then. While the Mac probably hasn't gained much marketshare since then, the popularity of the iPod and iPhone have given Apple a pretty solid foundation right now. In the short term, I don't see Apple having any problems, but the real question is if Apple's new leadership would be able to keep this track record going.