Can't speak to today's charts, but such precipitous drops were commonplace in the '60s and '70s. The journey down the charts was nearly always shorter than the trip up. Makes sense -- stations put songs that were new, hot and "pushed" in heavy rotation; once they'd reached their peak (in sales, listener requests, etc.) there was no reason to keep playing them much longer, so down down down they went, into very light rotation until they just weren't played anymore. No one really minded because by that time there were 10-20 newer songs driving the format.
Extreme example: Dionne Warwick & the Spinners' "Then Came You" (1974) plunged from No. 1 one week all the way to No. 15 the next.