Wasn't PSX the official acronym of the Playstation up until Sony up and released a real PSX, which was a PS2-based media box? Then all our PSX abbreviations were thrown a loop.
I could be wrong here, but I want to say that once the PlayStation became the PlayStation and not the machines that was a subset of the SNES, the "X" was dropped. I did a one-shot PlayStation fanzine when the machine was first hitting the States, and I almost want to say that in talking to Sony, I was told at that point that PSX wasn't "proper." Even if it wasn't that early, I do seem to recall somebody from Sony stating in some publication or something that "PSX" was not a Sony-recognized abbreviation for the system.
Again, I could be wrong, but I don't think Sony themselves ever officially used PSX in reference to the PlayStation ever, at least publically. Pretty much everybody else was using that abbreviation, though, so I think that's why it stuck as much as it did. To this day I still use it, even though some people now like to say that it's wrong.
I was under the impression that the PSOne we know now was referred to internally at Sony as PlayStation-X to not confuse it with the original Super Nintendo based PlayStation.
I remember reading in magazines a lot of them were referring it as PSX/PlayStation-X for a while prior to launch. I guess it just stuck.