Have you always been living in that house?
Is it grammatically correct?
Yes, but much more natural is Have you always lived in that house?
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"have you always been" can be found only 84 times in fraze.it, Google Ngrams, and COCA combined. There is only one case among those 84 where it is followed by a verb in the -ing form, and that one is in a very awkward sentence.
It seems that questions of this kind (present perfect continuous with 'always') are almost never used. I recommend that you not use that combination.