Nobody can really say. There isn't enough detail in the question.
One possible problem is that your Django app that "uses Twisted" does so by running Twisted in a subprocess or a separate process. Maybe your Apache stuff is re-running your whole Django script but there's a Twisted process off on the side that keeps running?
Alternately, maybe some part of your deployment infrastructure is calling reload() on your Django modules but Twisted is in some other thread and therefore not affected by that?
(Please consider attaching an SSCCE to this in order to give respondents something to go off of.)