What it means for an OS to succeed or fail
When we say that an OS has succeeded or failed, what we broadly mean is that it did or did not catch on. An OS that succeeds is one that makes sysadmins want to use it more and more, an OS that spreads and grows. Conversely, an OS that fails is one that does not grow; usage either shrinks or stays static. You can look at this both globally and locally, but we should always remember that in the end the global is the aggregate of a whole lot of local decisions.
(Here I consider each different Linux distribution to sort of be a different 'OS'.)
It's important to understand that your use of an OS doesn't have to be a failure in order for it to fail. In fact, to fail is kind of the default state of an OS simply because there are so many of them (and it's crazy to try to use them all). There's a whole spectrum of reasons that OSes fail to catch on in any particular place, ranging from them blowing up on you (an actual failure) through the OS simply not being different enough from something else you're already using (ie, it fails to have a sufficiently compelling reason to use it).
Each organization and group is different, so it's common for an OS to succeed at one place and fail at another. Sometimes this is because your needs and priorities differ, so that something that matters very much to you doesn't matter to someone else and vice versa. Sometimes this is just a matter of which specific OS from a group of sufficiently closely related OSes got a foothold at your site first (for bonus points, what OSes cluster together this way depends on what your needs and priorities are).
(Since it's hard to accept that your preferred alternative won or lost just because of randomness, the latter is a situation that easily leads to vociferous debates among the adherents of the various OSes.)
Locally, we've dabbled in a number of OSes over the years. Very few of them have been actual failures, where the machines we built just didn't work out, but almost all of them have failed in this broader sense in that they have not given us any desire to make further use of the OS. Sometimes we are just indifferent and uninspired by the OS; sometimes we turn out to more or less actively dislike the OS or find it a pain in the rear. Right now I think that only two OSes could really be counted as successes here (in that they are the two OSes we reach for automatically when building new machines), and I don't think we're entirely enthused about one.
(Note that you can still wind up using a failed OS. A number of the OSes that have failed here are (still) running today as vital parts of our production infrastructure. But their use has never spread and we are not too enthused about them. Succeeding and failing here is about changes in usage, not usage itself.)