Will we be able to download the backer beta multiple times on different computers? I'm not sure how much longer my current rig will be able able to survive. If I can only download it once, should I wait until I get something more durable?

There is no reason why it would not be possible. Gog and Steam treat the Backer Beta as a regular game and you can download those as often as you'd like.

Will we be able to download the backer beta multiple times on different computers? I'm not sure how much longer my current rig will be able able to survive. If I can only download it once, should I wait until I get something more durable?

Hello again cheesevillain!  Sorry to hear about the problems with the rig.  The good news is Sonntam is absolutely right   The game is added to your Steam or GOG account(depending which you choose) via the code you are provided in the Backer Portal.  The Backer Beta is currently only available on Windows, so the new rig would have to be running that operating system.  Thanks for reaching out to us!