Why can't players join my game any more, and how do I reopen it?

Registration closes as soon as you publish the rosters, not when the match starts. While the squads are split and confirmed, the game shows Registration closed and nobody new can sign up. That is deliberate: the teams are already balanced, and a late arrival would unbalance them. Registration also closes for good once the match is actually started, and that cannot be undone.

To let people in again, open the game and use Let players join on the Registration closed banner. Playbox warns you first, because reopening deletes the published rosters and any matches generated from them, and you will have to split the teams again afterwards. You can hide that warning for the future with the checkbox in it, while the banner itself stays, because it tells you the state of the game rather than reminding you of anything.

This applies to pickup games. In a team draft the slots are teams rather than players and they run out on their own, and in a league the squads come from the applications, so neither has this state.

You set the match length and rotation (Round-robin, Winner-stays, Swiss) when creating the game, with Winner-stays and 3 teams the winner stays on and teams rotate, which changes how rounds are scheduled. If the match “won’t continue after the first game,” check the rotation/round settings for that mode.