To be useful for quantum computation, gate operations must be maintained at high fidelities over long periods of time. In addition to decoherence, slow drifts in control hardware leads to inaccurate gates, causing the quality of operation of as-built quantum computers to vary over time. Here, we demonstrate a data-driven approach to stabilized control, combining extremum-seeking control (ESC) with direct randomized benchmarking (DRB) to stabilize two-qubit gates under unknown control parameter fluctuations. As a case study, we consider these control strategies in the context of a trapped ion quantum computer using physically-realistic simulation. We then experimentally demonstrate this control strategy on a state-of-the-art, commercial trapped-ion quantum computer.