the 45 seconds to death is often repeated but it is rubbish.
Depends on your height when you lose the AH.
Observed an overconfident businessman who owned his own Cirrus, in a flying school "simulator" practicing holding patterns. During the holding pattern inbound turn his instructor failed the AH without telling the student. He never picked it until too late and it turned out he couldn't be bothered to practice on limited panel (Turn Coordinator) as he claimed it would never happen in a Cirrus. . Within 45 seconds his VSI was off the clock in a steep spiral dive and I can testify he would have crashed as he was clueless what to do. The instructor mercifully "froze" the simulator when all was lost.
I recall 20 + years ago reading a BASIS report of a Mooney over- flying Mildura (?) from Adelaide on very dark night when the vac pump failed; thus AH failure. He reported having difficulties with his AH and that he would do a 180 and land at Mildura. He never made it and broke up in mid-air trying to fly on the turn indicator. That 45 seconds to death wasn't far off. No turbulence - just pitch black outside and probably never practiced limited panel instrument flying.
If you don't believe me check this link:
https://www.atsb.gov.au/publications...199703221.aspx