Your performance history stays with you. Rider-level data is held against your CicloZone account, not the studio's.
What happens
The studio loses access to the CicloStudio platform.
Your CicloZone account is unaffected. Your FTP, ride history, badges, and analytics remain on your account.
You can keep using the CicloZone app at any other CicloZone-enabled studio by entering its studio code.
You can keep using Home Ride, CicloTV, and Free Ride as before.
What you might lose
The studio's leaderboard data is live only and is not stored — so there's no historical leaderboard from that studio to lose.
Any classes the studio had specifically built for you in their Studio Library will no longer be playable through their account (but the Ciclo Library is still available everywhere).
If you want to keep riding
Just enter the studio code of any other CicloZone-enabled studio when you next join a Studio Ride. Your account picks up where you left off.