I believe I'm seeing the same issue. Here are some examples.
On our Tekkit server, we have a nether ice road for rapid traversal of the world. I've set up each branch with a nice ComputerCraft monitor sign with a "startup" program on the labeled computer below that sets the text. None of these chunks are forceloaded, but they do of course get loaded often as people travel the road, and eventually unloaded by Minecraft. Sometimes the signs look correct and have their text. Other times they are blank and the attached computer also appears off. Right-clicking the computer boots it and starts up the program. (I did have them behind the wall, but had to expose part of them so this hack-fix could be done.) Also, sometimes the monitor blocks will apparently be facing the wrong direction, which is a client-specific condition. This seems separate from whether the program is running and the text is displayed or not. (The text can be over the side texture of the monitor in that case.)
Another instance of the not-starting-up problem is in a factory I've put together. A labeled computer's program "startup" handles distribution of fabricated uu matter into different portions of the factory to create the raw materials for solar panels in the correct ratios. The program uses the "http" API to report the flow of uu matter to an external program (monitored through a AJAX web page). The chunks containing the computer and the factory are loaded by chunk loaders. Both World Anchors and Dimentional Anchors have been used. The server is set to reboot twice a day (3am and 3pm my local time). During the reboot, my monitoring web page notes the lack of updates. When the reboot is complete, the computer resumes communications with the web page. But after a few minutes, this ceases. Visiting the computer in-world shows that it is off, and a right-click is required to restart it and get the program running again. I'm posting this at 2:20pm my time, so in forty mnutes this should repeat itself, as can be seen
here. The "Time since last update:" value will be red if communication with the computercraft program has ceased for over a minute. I'll eventually ask someone who's online to take the ice road over and restart the computer after verifying that it is indeed off.
[That link is a work-in-progress and will not necessarily still be there in the future, so archives of this thread will probably not have access to it.]
I've been unable to think of any way to get it to auto-restart, and upgrading to a newer version of CC (as much as I'd like to) is imppossible given the large number of people that rely on Tekkit to make managing mods simple. Until Tekkit updates, we must continue to use this version. The only code update that could possibly fix the issue would have to be a server-side-only change to the 1.33 version (a 1.33r2 or some such). I'd be happy with a config change or something that can be done in-world to prevent this, if such is at all possible.
Thanks,
~ Nonsanity