Killing your games should be viewed as part of your standard operating procedure, not as a tragedy.
If I'd never abandoned a game, I would never have gotten to my best ideas. Killing games makes space for you to try better ideas.
Is your game an excellent game that can compete with the top 100 on BoardGameGeek? If not, abandon it. You should be trying to create a hit game, not a slew of publishable games.
Early on, I made every game with the intention that it was going to be completed. It made me sad when I was forced to abandon them. These days, I view game designs as experiments, with the full expectation that they won't survive.
Abandoning game ideas like this, after one play, is a normal part of successful game design. Expect that any given game is likely to be abandoned immediately. Don't feel bad about it. The most successful game designers have done hundreds of these little experiments.
Failed prototypes are also a valuable learning exercise.
Are you working on too many games? If you're working on more than two games at once, you should definitely kill the rest, and just work on the two that have the most potential, or value to you. That's what's going to happen in reality, anyway, so it's best to formalise it. These days, I only work on one game seriously at a time. I'm very excited to finish off the current game, because I can start on my shiny new idea! If I do both at the same time, I'll want to work on the new game, and have no motivation to work on the old one.
If a game gets bogged down, and I step away from it, it will never recover. It's hard to return to a half-done game design after a hiatus, because you don't understand what you were fixing (or what happened in the last playtests), and what issues there were. If I'm not planning to abandon a game, I always make sure to leave a game in a "ready" state, ready for the next playtest, and with some notes.
A "game graveyard" is not just a place of wastage. My game graveyard is a library of ideas and mechanics I'm increasingly drawing on. Once I've cannibalised mechanics and ideas from these old games, the new game is effectively a superior version of the old one, and the old one is just a source of spare parts. Such games will obviously never see the light of day, and they now make up the majority of my abandoned games. It would be nice to have every project see publication, but I still find it satisfying to have an abandoned project see fruition as a contributor to a successful, published game. The unique ideas that could've been amazing in their own right are harder to let go of.
Make lots of games. Kill them. The path to publication doesn't involve creating one game, and then working on it until it's "good", it involves making dozens of experiments, killing them, learning things, and eventually making something great.
Stop treating your ideas as valuable.
If having a published game takes five years and twenty abandoned projects, are you still interested in having a published game?
If you're serious, you should be killing the vast majority of your games. Get to it.
I've recently taken to doing what I call "one-day designs". I design, fill out, and do the work to create a playable prootype in one day only. I've got two of these already done, and unplayed. I'll play them when I'm not working on something important. This time limit, and the delay before playing them, gives me zero emotional attachment to these projects, and no incentive to make them nice, or waste time. I might actually create some more.