Wow, I missed this thread the first time around. Like others in this thread, I’m always trying stuff out and then deleting it, but that doesn’t really count. In terms of apps I used for prolonged periods and then said goodbye to, there are just three I can think of off the top of my head:
FreeHand. Originally when it was Aldus FreeHand, then through Macromedia FreeHand, until finally Adobe swallowed it up and killed it
I loved FreeHand. I always found it much more intuitive and easier to use than Illustrator, and frankly, more accurate - when I positioned something in FreeHand, it bloody well stayed there. And its guides/grid usage was sublime. I’ve been using Illustrator (because FreeHand is dead) for years, now, and I still can’t seem to “click” with it the way I did with FreeHand. Alas 
OmniOutliner Pro. I realised the other day that I haven’t actually used it for about six months. I mainly used to use it formalise complex outlines, after working them out on paper, and I’d still recommend it for that - it does it very well, and is a lovely, intuitive app. But I’ve just stopped needing it because of Scriv. Now I just do the paper stage, then go straight to index cards and folders in Scriv… because I can use those same index cards as the actual documents to work in when it’s time to script.
QuarkXPress. This was the hardest one. To understand just how hard, you have to know that before I became a full-time writer, I was a professional graphic designer for ten years, specialising in magazines and periodicals. I literally used QXP every single day of those ten years, and it was glorious. QXP 3.3 remains, imho, the high point of page layout on the Mac. It was blindingly fast, very stable, required tiny amounts of RAM, and did exactly what you expected it to every time. It Just Worked, to coin a phrase, and there was nothing I (and every other designer/art director I knew) couldn’t do with Quark 3.3, Photoshop and FreeHand on tap.
Then two things happened: the Web, and OSX. First Quark became obsessed with being able to create multilingual web pages (!) in XPress. Then they took an absurd amount of time - I don’t know exactly, but it felt like about three years - to release an OSX-native version. And when they did… it was utterly, unusably awful. An incredible number of bugs, unusably slow, bloated, massive memory requirement… and somehow they managed to do all this while adding absolutely no useful functionality. Unless you wanted to create multilingual web pages, perhaps.
Every pro I know now uses InDesign. Which, frankly, I don’t like, and I don’t know many people who do. But it works, and makes a sort of sense, which is more than can be said for QXP these days. They literally had an entire global multibillion-dollar market in their hands, and just threw it away. So, so sad.