This is a solution I found by myself:
(0) If you have passwords ONLY on the iDevice --> Sync the iDevice with the iCloud in order to save them
1. Uninstall 1Password from the iDevice
2. Install it again
3. Sync the iDevice with the Desktop App
(4). Sync the iDevice with iCloud and then again with the Desktop App in order to get the missing passwords in the Desktop App
Suggestion to the 1Password-Team: This solution should be described also here: https://support.1password.com/wlan-server-troubleshooting/.
Have a great day!
1Password Version: 4.6
Extension Version: .6.2.626
OS Version: iOS
Sync Type: WLAN
Thank you for sharing this with the community @Dimiter!