Hi there! I understand that you're having issues with the weekly ad not opening, staying logged in, and accessing your shopping list. Let's sort this out together!

1. Weekly Ad Issue:
- First, I recommend trying to clear your web browser's cookies. Sometimes, old cookies can cause issues with loading pages. Here’s how you can do it on your iPhone:
- Go to Settings > Safari (or your browser of choice).
- Scroll down and tap on Clear History and Website Data.
- After clearing, try re-opening the weekly ad.

2. Staying Logged In:
- Are you using the Publix app or the website? If using the app, make sure it’s updated to the latest version through the App Store. You might also want to try logging out and back in again.
- If you are still logged out, consider resetting your password by selecting "Reset your password" on the login screen. That may help keep your session active.

3. Shopping List Access:
- If your shopping list won't open, ensure that you have a stable internet connection. Weak connections can affect the app's performance.
- Again, clearing the app’s cache or reinstalling the app if necessary might solve this issue.

Let's try these steps and see if it resolves your issues. If it doesn’t, I can look up further specifics. Are you satisfied with the solution I provided?