mac mini's wireless setting keeps on reverting

There's definately a setting where you can list the order of Networks. You probably have that unsecured network at the top of the list, therefore it's the highest priority.

I'm not at a Mac right now, so it's hard to say where it is.

I think it's in the Airport or Network system preference pane.

 

So you're using a mini to create an ad hoc network?

By default this network style is assumed to be temporary, which would make it be reset upon restart.

what you could attempt to do, is create an alternate network profile, and then use that as the default profile.

That may correct it.