Many sites, including us run django and cope with several 100's of requests per minute, without issue, I've never had django become unstable or a single gateway issue. How did you try and host django?
You should monitor server behaviour and throttle traffic back when it's close to its limits. I usually see things on monitored servers (check memory allocation over time - how much cache, how much process, how much kernel, iowait time, swap for sharp increases) in time to issue corrective measures.
Tuning maximum processes/threads on Apache seems one simple way to prevent that. Memcache and Varnish are also your friends with that - anything that prevents the workload from reaching Apache is.