How do I record video for more than 30 minutes at a time with a Canon A1400 PowerShot?
Yes, CHDK should be able to do this.  There are actually scripts available on their wiki for this.  Basically, you have to tell it to press the video start button, wait a second or two for it to start, then begin polling to see if the get_movie_status has changed to the status for being done recording.  You then wait a second and repeat.

You'll also want to make sure you remove the 30 minute time limit with CHDK itself if available on your camera (under the video menu).  If it is, then you should only be limited by the 4gb file size limit and the script should restart the video.