Unless you backed them up it's not possible to download older versions. You can update Object Desktop to the latest versions at a discount.

https://www.stardock.com/products/odnt/

It's not 'rental'. As with most products available to purchase online...you purchase them....then you download them, and install with the provided/purchased key.  Process is complete.

If you wish to reformat and/or reinstall at a later date you will have needed to put that download and that key somewhere safe - and you can reinstall any time you like at your leisure.  The program and key will never expire.

That is the true meaning of 'purchase' - and not 'rental'....

No, the licence keys do NOT expire.

They will be valid for the program for which they were purchased for the life of the person and/or program.

A Windows XP Licence key is valid for ever, likewise.  But it is not valid for Windows 7.... the later version of the OS.

For 7 you need a new key, however that does not stop you using XP and its key.

The very same applies to Stardock's programs.

Example....Fences 2 is not Fences 3, just as XP is not 7.

I'm trying to think of a program whose key remains valid for all versions/releases of the program.   The closest I can get to is my Kaspersky Internet Security....but that's a SUBSCRIPTION service....3 machines by 2 years...then pay again.

Directory Opus....I'm still on version 10,5,7 because anything later wants a new fee and Code...but what I have serves the purpose just fine.

Acronis True Image 2019 keeps telling me there is a 2020 ...but that'll cost too [with key] so I can wait a few more releases before upgrade....maybe 2022 instead.

This is how computer software works...