The typical robber is stupid, impulsive, and antisocial. All of which are traits that contribute to low incomes.

There are relatively intelligent robbers who manage to pull off diamond heists and the like, but these are a minority of robbers and aren’t a threat to your typical local retail business.

Also, as crime becomes endemic in a community, anybody who can afford to leave does so. Businesses close as well, reducing economic opportunities for the people left behind.