This will be an unsourced answer. I imagine this has a lot to do with politics. Moses only goes back to Egypt after the Pharoah who wanted to arrest him dies, this leaves open the idea that Moses can't be convicted of having killed that Egyptian 40 years ago. This might explain why the new Pharoah never bring's up the Egyptian that Moses killed in the past.
So when Moses makes demands of Pharaoh he seems to be making those demands with the understanding he will not be arrested. And Moses's initial public demand is not "Let my people free," it was "let them celebrate a festival to our God." This is actually a reasonable, and probably lawful demand in Egyptian society. We know that Egypt had a forced labor class that was paid, had rights, and even organized labor strikes, so it makes sense that Pharaoh wouldn't kill Moses outright because that would make Pharaoh look bad to the royal court.
Moving on from there, Moses never threatens Pharaoh directly with harm. God causes all the plagues, even if Moses (or Aaron?) put on a little show while it happens. This gives the impression that even if Pharaoh decided to kill Moses/Aaron, the plagues might still keep coming, so killing them off wouldn't solve anything.