I've bought my Fluke 87 Meter new about 20 years ago. I love it, so today when I turned it on and it beeped continuously in every position of the rotary switch, I immediately searched for answers. I found manuals, but the continuous beeping was not mentioned.
Someone suggested replacing the input receptacle block, those run about $32 on ebay.
Instead I tried cleaning the receptacles with contact cleaner on Q-tips, there was a lot of grime in there, but it still beeped afterwards.
Looking closely I saw no cracks in the receptacle plastic or around any of the solder joints. But I re-soldered all of the receptacle solder joints using fresh solder, the idea being that there might have been hard to see stress cracks around a pin. And it worked. No new receptacle was needed.
Perhaps this will save someone else some time and money.