Depending on the venue, not repeating a song multiple times is as bad as playing the same song back to back.
I played in a little country band and we played places where dancing was almost as popular as drinking and whatever the current top country dance tune was would be requested over and over again all night. At first we would play it once then tell the girls requesting it we'd already done it. They would get all pouty and petulant and hang out at the stage trying to get us to do their favorite (at the moment) song again so they could drag Billy Bob back out on the floor to strut their stuff for him another time.
If the place was big on line dancing, we could have gotten away with playing the same two or three songs all night.
Point being, if you are hired as entertainers and if the people you are being paid to entertain want to hear the same song 4 or 5 times that night, you are being paid to make them happy, not enlighten them to your musical ethics and/or mastery of a song list so massive you need never repeat a tune on that particular job.
What is truly ironic is you will work the same room two weekends in a row and do the same set list, with maybe a few minor variations and not even give it a second thought, but the same song in the same night somehow implies a lack of skill or a slight to your honor as a musician?
When you are being paid it is for your skill as a player, but it is also for your ability to show the unwashed masses in attendance a good time. If that good time includes wanting to hear certain songs more than once, it is a testament to your skill as an entertainer to play them with a smile, even if it's twisting your panties so hard it hurts your ego something awful.