To be clear, here at 20Skaters we've built the platform to make your organizer's lives simpler. We do not have ANY ice time ourselves or run ANY pickup hockey. Our organizers are fully in control of their game schedules, player lineups etc.
If you have any questions about whether you're invited to a game or not, only your organizer can answer that for you.
I can offer some basic guidance....
If you are a paid, full timer in your game then you should likely be invited to all games on a regular basis. If you're not seeing your regular invite email then it's possible you're off this week.
If you are a sub in that skate and are not seeing your regular invitation email then it's possible the skate isn't running this week or the game may already be sold out and they don't need more subs this particular week.