Recording unscheduled programming

Today (for example), there was a major news event in the area that superseded all normal programming.  I really wanted to watch, but could not at the time, so would like to have been able to record a channel for 3-4 hours.  I could have gone in and set up recording of each individual show during this timeframe, and I assume it would have recorded those times with the changed programming...but what a pain and time waste!  Not to mention, now to watch the programming I actually have to watch 4, 5, 6 or more different shows that are recorded separately.

Is there some way to be able to record a channel for a period of time?  Or extend the time of a program (a great example here would be a sporting event that could go over by an hour or more!).  This is something we could do with DirecTV by satellite...I don't understand why we can't with streaming.  Definitely a BIG negative!