Of course NASA updates software mid-mission; they're famous for sending software updates out to deep-space probes and rovers to fix things as critical as communication issues, which is quite a neat trick.

What they don't do is allow updates to happen automatically. They're carefully pre-tested, and the update is carefully planned and scheduled. Their goal, like most enterprises, is to minimize risk, and bugs that you know about and understand the impact of are much less risky than updated software you haven't been able to test yet.