Many distros (like Ubuntu) terminate support of older versions. Others (like Damn Small Linux) support old versions.

Does antiX ever terminate support of older versions? I'm considering trying an older version, as the latest version (M8.2) doesn't work well with my old desktop computers.

I think the answer depends on what you mean by older versions. But before jumping back to any version older than the latest, why not describe the problems you're having with M8.2? Maybe someone here can help you diagnose the problem and help you get it running. You'll probably be happier with the latest antiX and have fewer problems than trying to maintain an older version.

Post your specs for the desktop(s) so we can help you better.

$ inxi -F

Apart from the first antiX Spartacus release (based on Mepis 6.5 and thus Ubuntu) all other releases are based on Debian and Mepis. You may get the older ones working better, but there is no support beyond Debian Etch (by Debian itself) nor for MEPIS7 repos. However, you should be able to keep it fairly up to date with a bit of tinkering.

BTW it appears that DSL is dead. A great shame, but no release since 2008.