Does anyone know why certain sites will appear and disappear on the same search depending on the time frame of the search? For instance, I've done a search one week and found one site, then two weeks later it's gone, only to reappear a month later. Any ideas?

Changes in the google algo and changes in the SEO of the page.

Another possible reason is that Google uses different servers and sometimes the results from one server will be different from another. I think over time the servers converge in the information stored on them, but it's possible to do a search and then the same search an hour later and see different results.

But StOx is right in that it's probably just changes to the optimization of the page or tweaks to the algorithm.

i guess its also possible that you are hitting different data centers and therefore getting different results