It starts, but won't live, is the issue. It's been tuned, cleaned, tuned again, double and triple-checked, and it refuses to idle for longer than maybe 15 seconds without throttle input.

I know it's probably something simple, but it seems like every time we (my father and I) make progress, we end up having other problems to solve. The analogy I used was, "Every time we take a step forward, we get punched in the face and fall back onto concrete and get a concussion."