We study optimal monitor placement for intrusion detection in networks with persistent attackers. The problem is modeled as a stochastic game in which the attacker attempts to control targets by delivering malicious packets while the defender tries to detect such attempts. The state of the game is determined by the target end-systems in the network, each of which can be in either a healthy or a compromised state. Compromised targets are controlled by the attacker and may be used to inject malicious packets into the network to attack healthy targets. In addition, a random re-imaging process is deployed on all targets to regain control of compromised targets. We find the game value and the equilibrium strategies for both players under different assumptions on the knowledge of the state at the defender.