Need help with Critical Path? Email mat.enrique.galicia@gmail.com and I'll get back to you.
Your runs and saved scores live on your device. If you use iCloud backup for your phone, they're included in that backup like any other app's data. Critical Path itself has no cloud server.
A few things explain this, all expected rather than broken:
You can check exactly what Game Center has and hasn't received from Settings → Diagnostics → Game Center.
From Settings → Diagnostics, tap Share to send a report — it includes what went wrong without sending anything else about you. Email it to mat.enrique.galicia@gmail.com along with a short description of what you were doing, your iOS version, and which scenario you were playing.