How do I keep design docs up to date?

You can write good design docs now. Keeping them current as the game keeps changing is a different battle, and it defeats a lot of people, because a document is a snapshot and the work never stops moving. The moment you finish, reality starts drifting away from what you wrote. The mistake is trying to keep everything perfectly up to date all the time. That is a losing race, and chasing it will exhaust you while the docs still fall behind. Not every part of a doc deserves the same upkeep. The core decisions and the reasons behind them are worth keeping true. The fine details will always lag, and that is usually fine. So decide what actually has to stay current and let the rest be a record of a moment. Keep the load bearing parts, the key decisions and why they were made, alive and correct, and update them at natural checkpoints rather than constantly. You are not failing to keep the whole thing current. You are choosing, on purpose, which parts are worth the upkeep. That choice is the skill, not heroic constant editing.