To ensure a stable tuning, you should regularly check all screws for tightness. This includes the mounting screws of the neck and the tuning machine mounts. Modern tuning machines are usually held in place by lock nuts, so remember to check these nuts for tightness as well.
It also pays off to apply some graphite dust (e.g. from a pencil) or a special lubricant like teflon oil to the saddle grooves once in a while. This lets the strings move freely across the saddle and contributes to a stable tuning.