How do you keep volunteers past the first three months?

Give them one thing that is theirs. Volunteers who are helping leave. Volunteers who are responsible for something stay, because it stops being your project and starts being partly theirs.

This matched our experience exactly. The two who stayed both had a specific job nobody else did.

Also ask them why they came. People volunteering to learn a skill need different things from people volunteering out of duty, and we used to treat both the same.