Elements repeatedly freezes about half hour into editing (new computer 16GB RAM).

The POS in this case is probably your video card.

Seems harsh, but it's generally the problem, particulalry with laptops.

Are you talking about Premiere Elements or Photoshop Elements?

Are you getting any error messages?

What kind of editing are you doing?

Are you using any plug-ins?

Are you using the Organizer?  If so, how many media files are in your catalog?

It is possible that Auto Creations are being created or media analysis is taking place in the background?  Try going to the Organizer's Edit>Preferences>Media Analysis dialog and unchecking all of the boxes.  Do you still experience the freeze?