I used to think my hearing was bad, but I've discovered it's more subtle than that.
The first sentence spoken by someone I'm not looking at is perceived as a meaningless string of syllables. It's right there in my short term memory, the series of sounds you just made, and sometimes, after I've realized you were speaking to me and I've looked in your direction, the sounds fall into words, the sentence you spoke. But more often, the string of syllables remains just that, or resolves into a string of nonsense words/phrases that sound like (or rhyme with) what you said.
I can even repeat it back to you, and it'll sound like a random string of syllables, or nonsense words/phrases, to you, too. Many times the result of the misparsing is almost art, and usually more interesting than what was actually said. :) We used to call this Immelitus, after a friend whose last name was Immel.
On the other hand, if I'm looking at you before you begin speaking, I'll understand you just fine. Sometimes I instruct friends or cow orkers to get my attention before they try to ask me something so I don't seem to be deliberately ignoring them.