If the browser is up then it's just a simple matter of calculating a time delay for the first occurance, and then setting up a routine to recalculate the delay after each subsequent run.
Is it also possible to use the meta http-equiv="refresh" tag?
<META HTTP-EQUIV=Refresh CONTENT="1440; URL=?">
I think what you're actually looking for is what's called a "cron job". You would be best to ask your hosting provider with assistance in setting it up and getting it sorted how you want. Just write your script and what you want it to do, then contact your provider aabout how they support them.
That's what popped into my mind, too -- a daily cron that did 'rm page.html'.