Looking on the internet deeply has found these results:

We have always been doing is the most popular phrase on the web.

we have been always doing 123,800 results on the web	We have always been doing 1325,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
She's always doing that, making people mad. Or Max is always doing something weird. So you know how Billy's always doing something crazy. She's always doing things as she pleases. Y'all so close, always doing everything together. Always doing things for other people, That's because you were always doing it. She was always doing what could not.	So the idea that we're always doing both at the same time is just not true. We are always doing our utmost to modernise our internal IT systems. I just feel like we're always doing whatever the girls want us to do. We have always been a committee with strong participation. Times as hard as these, and people go on doing what they've always been doing. We have always been able to celebrate defeat. Well, We Were Always Doing The Funnest Things. We have always been known for our progress.

we have been always doing

123,800 results on the web

We have always been doing

1325,000 results on the web

More popular!

So the idea that we're always doing both at the same time is just not true.
We are always doing our utmost to modernise our internal IT systems.
I just feel like we're always doing whatever the girls want us to do.
We have always been a committee with strong participation.
Times as hard as these, and people go on doing what they've always been doing.
We have always been able to celebrate defeat.
Well, We Were Always Doing The Funnest Things.
We have always been known for our progress.