"Public servers" are just servers run by people who don't put a password on when they start a community server. Generally unsavory to play on because of low brow human nature on full display. Rent a dedicated server or have somebody in your group built it/run it, then it can be up all the time. Unless you're ready for griefing, or are griefers yourselves, maybe your group should avoid random public servers. This isn't a MMO, if that's the experience you're looking for.