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I know that's frustrating but it's to protect your phone, you could disable all security features on your phone.
Hi @2xsony, Im sorry to hear about that and I understand that this must be frustrating. 
I'd recommend that you try and remove your Google-account from your phone in Settings > Accounts > Google > your email adress > 3 dots > Remove account.
You will have to authenticate when removing the account so make sure that you are connected to a Wi-Fi network and that you have your Google credentials at hand.
When the account has been removed restart your phone normally and add your Google account again in Settings > Accounts > Add account.
Restart the phone again and see if you have to authenticate again.
Let me know how it went! 
Hello again!
I'm sorry I forgot to mention that in my previous reply. 
You can deactivate it first and then verify with your Google credentials, then remove the Google account and restart your device.
Add the account again and activate the service under Settings > Security > Protection by my Xperia.
Let me know how it went! 
You would still be able to authenticate with the first Google account that was added in your phone, so no worries about that! 
How is working now? Is it still asking you to authenticate after rebooting your phone?
Let me know! 