In previous work, we have developed optimal-control based approaches that seek to minimize the risk of subsequent virological failure by "pre-conditioning" the viral load during therapy switches. These techniques result in the transient susceptibility of the total viral load, and rely on finding the minimum of a dip in viral load and switching before viral load rebound. Model uncertainty necessitates a closed-loop approach to minimum-finding. Blood measurements are costly in terms of money, inconvenience and risk. In this paper, we introduce an iterative parameter estimation approach to find the viral load minimum, and measure the degree of optimality of minimum-seeking under conditions of measurement noise. We evaluate the cost-savings of this approach in terms of number of samples saved from a constant measurement rate.