At an old work-site I heard alarms that went off too frequently described as "chattering alarms", which is the best term I can think of so far.
Chattering alarms (alarms that repeat excessively in a short time interval) create a level of nuisance to the operator. - src
However it's not quite right because I'd like something that maybe captures how it becomes ignored.
I also don't particularly mean it in a "boy who cried wolf" scenario in that eventually the alarm will be important, moreso just that when someone's constantly being warned or advised, they just tune it out as insignificant.
Thanks in advance!