According to the article Significance of the stapedius
reflex for the understanding of speech, the latency of
contraction is only about 10ms, but maximum tension may
not be reached for 100 ms or more.[6] According to the
article Le traumatisme acoustique, the latency of
contraction is 150 ms with noise stimulus which SPL is
at the threshold (ATR), and 25-35 ms at high sound
pressure levels. Indeed, the amplitude of the
contraction grows with the sound pressure level stimulus. 10]
Because of this latency, the acoustic reflex cannot
protect against sudden intense noises.[10][6] However,
when several sudden intense noises are presented at a
pace higher than 2–3 seconds of interval, the acoustic
reflex is able to play a role against auditory fatigue.[10]
I did not bother to check more than the abstracts of the references, but it does seem like evidence exists.