My gut tells me this is a permissions issue.

Well, search  was working  on Friday. Is there a way to STOP
the "Pausing?" Is there a service that I can stop to rectify this
pausing status?

Check gatherer log after doing full update(site settings>configure
search and indexing  page).

If gatherer log errors and the below errors are same , then implement
the steps given in the article

support.microsoft.com/default.aspx

I came in this morning and Search isn't working. I see in my Content
Sources under SSP>Search Settings that all of my Content Sources
are "Pausing". I can't get them to unpause. Is there something that I'm
missing? I remember reading somewhere that if a crawl is going when our
backups are running, it'll put the crawl into a "Paused" state, but
then I could just resume the crawl. Here I can't do anything.

Is there a service that I need to restart or something?

Well, search  was working  on Friday. Is there a way to STOP
the "Pausing?" Is there a service that I can stop to rectify this
pausing status?

Search is such a pain in WSS 3.0. It happens to our box ALL the time
and I can't figure out what causes it. The sure fix is to stop the
search service FROM CENTRAL ADMIN or via the STSADM cmd line(killing
the index) and then start it again. Make sure you are using the right
types of accounts for each role...

If you have trouble killing the search  service via the central admin
page or stsadm... then I'd figure out the pid of spsearch and kill
that. Hope this makes sense.

I don't know why search dies but at least I can reliably put it back
very quickly. If I'm wrong on this or there's a better way.. let me
know. I'd love to not have to do this ever again.

Be aware that stopping the PID (think Windows Server Service) only stops
the engine on that box. Stopping Windows SharePoint Services 3.0 Search
from Central Admin turns it off in the configuration database.

Two very different actions. I would suggest merely restarting the
Windows Server Service and see if that fixes it. Turning it off in
Central Admin resets and rebuilds the index.

I should have been more specific... if you CAN'T get the search
service to stop (which for us happens a lot) THEN you can resort to
killing that process ID. If you've ever seen your search  service
remain at "Stopping" and never get to "Stop" you'll have to kill the
process and then try stopping it again.

That is what I had to do. Nothing I did seemed to stop it. Thank you
all for your advice.