Hey everyone!
I wanted to share what seems to be working for me, based on about a month of okay-ness so far.
I tried nearly everything listed in this (and other) threads, and was disappointed to see photo stream get turned off reboot after reboot.
Then I read one post (I forget where) the problem was fixed after rebuilding spotlight. That didn't fix it for me either, but I noticed that for a short time after rebooting, my mac would say it was reindexing some stuff.
As long as I started Aperture while that indexing was taking place soon after boot, photo stream would not be on. A lot of the helpful suggestions people have posted involve rebooting, and of course we all launch Aperture immediately after to check. I think this is why a lot of us keep encountering this problem!
Since then I've only turned Aperture on a good couple minutes after my mac reboots. (On OSX > = Lion this means making sure Aperture is closed when you restart, or that you turn off the option to have applications automatically relaunch when restarting.
I hope that's useful to someone out there.