My site status reports:
Boost crawler did not get a 200 response; 403 returned instead. Forbidden Menu item for crawler is not there. You need to "Clear cached data" at the bottom of the performance page

I've tried clearing every conceivable cache and reset the crawler multiple times, but the error won't go away and nothing is cached on cron. If I go to the URL http://path/to/site/boost-crawler?nocache=1&key=[my_key], I get a blank white page and a log entry from Boost that reads "Crawler - Rogue thread killed."

I don't know if it has any bearing on this, but my site is running behind a load balancer and http requests go through a web proxy. To support this, I've applied the patch from #735420: Drupal 6 proxy server support. From what I can tell, this patch is working as it should. I am able to check for module updates and prior to the patch Boost was throwing a completely different error on the status page.