Seems Beta Search does not provide information for upcoming showings of a program while it is currently being aired. At least some of the time.
I was in the middle of watching a show on HDNet this morning when the TiVo had to change channels for a scheduled recording. After the TiVo changed channels I went to the Beta Search to look for upcoming showings of the program I was watching on HDNet. The Beta Search gave me the option to watch the program live, but no listings for upcoming showings. Knowing it was unlikely that HDNet would air a program just once I went to the standard title search and did indeed find a subsequent showing.
I tried with some different shows with varying results. For Dreamgirls, the Beta again did not show upcoming results during a current airing. For 30 Minutes meals, which airs at least once a day, the Beta did show upcoming results during a current airing.