First, go to your device task switcher, shut down the app and relaunch fresh. Does that fix the issue?
If not, next things to check for troubleshooting - first, if you go into settings, then notifications, is the notification location setting set currently?
If you go to your device settings to apps, to 1Weather then to permissions, is the location permission active?
If you check those and still see the issue, where exactly in the app are you seeing the incorrect date(s)?
If so, if you go into your device settings to applications, to 1Weather, and then tap "Battery" are any of the power saving options on in that location?
If you go to settings --> Battery is 1Weather optimized under App Power Monitor? Is 1Weather listed in Unmonitored apps? If not, try moving it into Unmonitored apps and see if that helps.
Usually if the app isn't updating, and it's not due to one of the first two items, it's due to the app getting shut down in the background by one of the Android power saving services.
If you need further assistance, please launch 1Weather, tap the menu and select Help --> Contact Support.