My action stream is updating on the MT backend, but not on the website front end, which has the info from when I set things up a couple of days ago: http://www.alesh.com/
This can't possibly be a problem with the cron job, can it? What else could be happening??

Hmph; thanks for nothing, folks.
Glad I use Textpattern for stuff that really matters to me.
Here's a few things it could be:
* permissions issue
* template tag error
* cron error
* plugin conflict
* out of date plugin
There is a setting in your Action Streams plugin settings area that you can toggle which will automatically republish index pages when new actions are aggregated.
If this is not working, I have sometimes found that a faulty connector to a service can cause AS to completely bomb out in the middle of the update.
Have you added any services recently? You might consider removing them temporarily and see if that helps.
Thanks Byrne, that was it!
It took me awhile to find, because the "rebuild" option is unavailable under the plugin page in "system overview" mode, only in the page for the blog.