I don't really know what's normal as I've only sold one house in my life. But I think it's normal for offers to have some expiration date, so you can't just keep stringing a buyer along while you wait for better offers to hopefully roll in.
When my brother sold his condo in Washington, DC, someone made an offer before he had his first open house. But the buyers stipulated that my brother make a decision on the offer before the open house. Of course, to make it worth taking the unit off the market that quickly, it had to be a strong offer, and it was.
Mind sharing a link to the listing? My wife and I love real estate porn.