Is that ironing going to take you forever(=for all eternity)?
"Aren't you ever going to finish..."
'ever' : at any time, an actual time when = is there going to come a time when you will (actually) have finished the ironing?
'Aren't you going to finish the ironing anytime?' doesn't make sense, nor does it convey the astonishment conveyed by the question, that the ironing seems to be taking the person forever to do, far longer than the speaker expected.