Check those switch and Turn ON:
1. Settings->General->Background App Refresh->Wi-Fi or Wi-Fi & Cellular Data
2. Settings->Sync Contacts->Background App Refresh->ON
Use Background App Refresh
After you Turn ON, this app run for a short period of time before they're set to a suspended state. With Background App Refresh, it can made vCard file and email to your account.
❗️ If you quit this app from the app switcher, it might not be able to backup before you open it again.
❗️ It might not be able to backup if your battery life is short.
❗️ It is not backup when your device is offline.
❗️ It was backup but can NOT send email because device can NOT connect to Gmail SMTP server.
We test passed on iPad mini 2, iPad 4, iPhone 6, iPhone 6 plus, but failed on iPhone 5.
💦 We strongly recommend that you set up your own SMTP server.
It is more secure and faster.
After setting up you own SMTP server, your backup email will be sent from the email account.
We have tested some mail servers, including: