The invoice date will not automatically change to yesterday's date or another particular date.
I'd like to know if you're able to do the app troubleshooting steps, such as uninstalling the application to start with a clean slate? If you haven't done it yet, I'd suggest performing it to remove any data issues.
Here's how you can uninstall the QBO app on your phone:
Go to the Settings and select Apps.
Locate the QBO app and tap Uninstall.
After that, you can restart your phone and then reinstall the QBO app. I've added the links to the App stores for Android and IOS: