Designer, I think it is a stable site.
I have used the resource for several years with good results most times. Once a page is archived there, it stays there.
In my cyber wanderings, I encounter tons of links that are dead with previously available material no longer at the link address. Often, I have been able to access previously archived pages and resurrect old material. It is awesome for sites that try to hide or change their info.
However, the Wayback Machine doesn't capture everything - some web addresses have few or no pages archived. It seems that the more traffic a page or site gets, the more often wayback will take a snapshot and archive it.
Archive.org - and the Wayback Machine on that site - is one of the most frequent and reliable sites on the web that I use.
Have fun. A person can dig up a lot of old treasures on that site.