I'm having the exact same issue.
Having a phone is quite literally a life and death necessity for me.

This is a serious issue.
The fact that so many people have it across totally different networks in different countries suggests it is a problem with the phone.

There is no evidence of it being a problem on the phone until you try to make a call.
This started happening for me yesterday.

I have the latest firmware update.

The big problem for me is that there's no noticeable problem - you can't tell if this issue is happening. So if people are phoning me, I won't know if they can't get through.
And if I suddenly need the phone in an emergency and it doesn't work, I'm stuffed.

Since this seems to have started only very recently, could the latest firmware update be at fault?