That was the question posed by an anonymous reader to the folks at Grammarphobia. This person noticed how, in old movies (pre-1950s), people used to say that they would be stopping at a hotel, but these days, we would usually say that we will be staying at a hotel. So, he sent in the question.
Apparently, the use of "stopping" has not yet been phased out as the team at Grammarphobia found someone who had actually used the expression quite recently. A British tourist had posted something to that effect on TripAdvisor. It's not grammatically incorrect, just unusual perhaps these days.
According to their research, the usage of both expressions were fairly equal until the 1940s, when "staying" saw more widespread usage. Why that was the case was perhaps out of the scope of the question, but one can only surmise that "stopping" just doesn't have the same feel as "staying" does.
However, there was an article in The New York Times which used "stopping" to mean "staying" but as a pun. It read, "Stopping at the Savoy", which was a reference to Edgar Sampson's "Stompin' at the Savoy". Language is quite fluid, and it changes along with those who use it. Maybe the expression just fell out of use. -via Strange Co
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