To fall down in great numbers: All over the hot theater people were dropping like flies
[1940s+; like flies meant ''in great numbers'' by 1595]
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with drop like flies
Rapidly collapse, die, or drop out, usually referring to a group rather than an individual. For example, The words were so difficult that the spelling bee contestants were dropping like flies. The simile like flies has meant “in large numbers,” as it does in this expression, since about 1600.