Cleveland radio station WDOK removed the song from its list of holiday music after objections from listeners, host Desiray McCray told local media last week.
However in an online petition by the radio station 94% of respondents said they would rather keep the song and only 6% argued that it was inappropriate.
Many furious listeners were so horrified at the station's decision that they threatened to boycott it, branding those who wanted the song removed "snowflakes".
The song, originally from the 1949 film Neptune's Daughter, is based on a male singer attempting to dissuade his date from her attempts to leave his house by arguing that the weather is bad.
It includes the female singer saying lines like "I really can't stay" and "baby don't hold out" - which many people regard as creepy and suggestive of sinister sexual coercion.
"When the song was written in 1944, it was a different time, but now while reading it, it seems very manipulative and wrong," WDOK host Glenn Anderson wrote on the station's website.
"The world we live in is extra sensitive now, and people get easily offended, but in a world where #MeToo has finally given women the voice they deserve, the song has no place."
Special criticism has been reserved for the line "say, what's in this drink", which has been accused of carrying the implication that the woman's drink has been spiked.
But some have argued that in the context of the 1940s the song dramatises a the speaker's struggles against her desire to stay and the social expectations that would shun her for staying overnight.
In the original movie the roles in the song are also reversed: after the better known version is performed by Esther Williams and Ricardo Montalban it is repeated with Betty Garrett singing the pushier part and Red Skelton pleading for the night to come to an end.