CST hasnt been showing much, if any, live midweek baseball. If they have, its been Southern for the most part with a little bit of Arkansas every once in a while and that's like a game every other week. Looking at the past schedule, they dont do LSU or Tulane midweek.
http://www.coxsportstv.com/program-schedule/2010/04/27/
Just guessing, but its probably not about excuses that come during the season. I'm sure they decide before a season to sign contracts with certain schools to broadcast games.