Hi there! I understand you're having trouble playing previous day puzzles on the Cryptogram app, and it's showing a "No internet connection" error despite presumably being connected. Let's get to the root of this and get you back to playing.

First, just to clarify, are you able to use other apps or browse the web on your Mac without any internet issues? Also, are you using any VPNs or firewalls that might affect the app’s connectivity?

Meanwhile, let's try some steps that usually help with this kind of problem on a Mac running OS X 10.15.7:

1. Restart Your Network Connection:
- Turn off your Wi-Fi from the menu bar.
- Wait about 10 seconds, then turn Wi-Fi back on.
- Try opening the Cryptogram app again and see if it connects.

2. Restart the App:
- Quit the Cryptogram app completely.
- Re-launch the app to refresh its connection to the server.

3. Restart Your Mac:
- Sometimes system processes need a reset.
- Click the Apple menu and select “Restart.”
- After reboot, open the app and check again.

4. Check App Permissions:
- Go to “System Preferences” > “Security & Privacy” > “Firewall.”
- Make sure the firewall isn’t blocking Cryptogram.
- Also, verify in “Network” settings that any proxies or VPNs aren’t interfering.

5. Check for App Updates:
- Is your Cryptogram app updated to the latest version? Sometimes connectivity issues are fixed in updates.
- Visit the Mac App Store to check for updates.

If after these steps, you still get the "No internet connection" error when trying to access previous puzzles, the issue might be either with the app servers or how the app handles offline caching of past puzzles on your device.

To isolate that point:
- Are you able to play the current day's puzzle without errors?
- Does the error occur only when accessing puzzles from prior days?

Last, if your internet works fine elsewhere and the app still insists there's no connection, occasionally Cryptogram requires a forced logout and login to refresh its authentication—if you’re comfortable doing that:

6. Log Out and Log Back In:
- Inside the app, log out from your account.
- Close and reopen the app.
- Log back in and try accessing previous puzzles.

Let me know which of these steps you’ve tried, and the results you get. That way, I can help with a more tailored fix!