There are examples of politicians who do well in tough districts or states despite not conforming to the DC notion of "Moderate." I'd guess spending time in your district, good constituent services, and supporting some genuinely popular things instead of fake-centrist things are probably how they manage to do it, even as Rahm's children and grandchildren get flushed out in every wave election.
The "moderates" who do stick around are actually in pretty safe seats, generally, and absent primary challenges will stay there. They're popular within the party because they raise lots of money.
