Yup, little brother number 3 had that. He got better... after a year or so...
I guess I can call myself fortunate. Worst ones we had were one colicky baby and one baby that would NOT sleep through the night for about the first three years of her life. I actually slept on the floor in the boys' room for a year or so 'cause I couldn't hack it anymore. Every morning at two or three she'd wake up and scream for no reason.
We tried keeping her up during the day to no avail. Did make for some comical dinner performances, though. She'd literally be nodding off in her mashed potatoes sometimes.