Apache continues to hang...help!

Ugh. Apache seems to be hanging at least once a day, requiring me to log into the server via Webmin and restart it. Here's where we stand:

* I'm running my web server in a VM instance on my own dedicated server. I have 2GB allocated to just this one VM instance.
* I get about 100K views a month.
* I've got plenty of PHP.INI memory limit set to 32, but the WP_MEMORY_LIMIT in wp_config is set to 64

I had thought, possibly, MySQL was failing, but stopping and starting MySQL did not resume web services. However, starting and stopping Apache (without a reboot), immediately restarted Web services.

I'm running two instances of multi-site, one powering zatz.com and its five associated tech article and news sites, and one powering zdecade.com, which right now just hosts trackyourcandidate.com and davidgewirtz.com (both of which get minimal traffic).

Since these are now live sites, and I've removed all the development plugins, I can't just go turning off plugins to see if that's causing the failure. I did spend quite a bit of time hunting down previous memory usage surges and found them to be caused by robot activity, but I tuned Apache to handle robot hits by turning keepalive off, setting timeout to 40, and setting:

<IfModule mpm_prefork_module>
    StartServers          3
    MinSpareServers       3
    MaxSpareServers      10
    ServerLimit         25
    MaxClients          25
    MaxRequestsPerChild   50
</IfModule>

So, I'm out of ideas. My next (very crude) idea is to set up a cron that simply turns Apache off and then on every four hours or so -- but that's a sucky way to go.

Advice and input would be greatly appreciated.

--David

P.S. Moving to nginx isn't an immediate possibility. I have a massive URL rewrite operation going in that rewrites my 100K+ URLs from old CMS format to new CMS format (that runs in Perl -- and no, it doesn't leak -- I tested it brutally and extensively).