I have my Action Streams on a Page, which has its archive type set to be published in the Publish Queue.
In the blog's Action Streams plug-in settings, I have "Enable rebuilding" checked.
I have run-periodic-tasks running every 15 minutes.
The only problem is that it doesn't get rebuilt. I do see new actions being imported every hour or so in my user's Action Stream section, so Action Stream is being triggered as intended.
Any ideas why it's not automatically rebuilding the page?
Reported on Movable Type 4.2

Try setting the rebuild type as "static." That's how I did mine, and it works fine for me.
I tried that and it worked initially (the first time), but stopped again. It only updates periodically, sometimes getting outdated for days before I manually publish it.
The actions are being imported regularly as that's always up to date... it's just the page that isn't. Odd.
It's possible that your host is killing the operation. How long does it normally take you to rebuild your indexes? With my host, anything over 20-30 seconds is in danger of being killed in my experience.
Just manually published that page, which took 12-15 seconds.
The catch is, the "rebuild indexes" property apparently tells ActionStreams to rebuild all of the index templates.