I have news regarding this issue.

In fact I was able to keep using the phone by jailbreaking and install Insomnia, which prevents phone from running in low power.
I used it for a week now but, as expected when using Insomnia, battery wouldn't old much, but still, good enough for my daily usage.

Today by mistake, I have left iphone without Insomnia and when I waked it, it actually did work. I immediately though that the application was running in background and decided to restore the iphone, to be sure there was no Insomnia app.

From nothing, it stopped turning off when in standby.

I would recommend you to do the same, it might happen that you get as lucky as I did. ;-)

Good luck