A few reasons.
As a rule, things having to do with astronomical objects take a LONG time to happen. Space is big, and at the speeds things move at they take a long time to cover the distances. When you're talking STELLAR scale its only over a period of YEARS that we can see things happen. Like this series of photographs of Barnard's Star moving relative to the more distant other stars (1/360 of a degree per year across the sky, fastest angular motion of a star in the sky)
http://en.wikipedia.org/wiki/Image:Barnard2005.gif . Most stellar scale things take WAY longer than that to see though. When we're talking planetary scale it still takes a while for things to happen - here's a timelapse series of photos from one of the voyager probes as it approached Jupiter
http://en.wikipedia.org/wiki/Image:790106-...31M_reduced.gif .
The time things take is not the only reason. Often taking astronomical photos means long exposures - you need to collect light for a long time in order to build up enough to make a decent image. As such, taking just ONE frame can take a long time. In addition, when you have data coming back from space telescopes or space probes, the downlink speed and onboard storage capacity is limited and is better spent on high-res images rather than low-res video.
There is, of course, LOADS of video from human orbital spaceflight and the Apollo missions and other satellites looking at the Earth. But as a rule those don't deal with astronomical objects other than the moon.