Emerging neural prosthetics require precise positional tuning and stable interfaces with single neurons for optimal function over a lifetime. In this study, we report an autonomous control to precisely navigate microscale electrodes in soft, viscoelastic brain tissue without visual feedback. The autonomous control optimizes signal-to-noise ratio (SNR) of single neuronal recordings in viscoelastic brain tissue while maintaining quasi-static mechanical stress conditions to improve stability of the implant-tissue interface. Force-displacement curves from microelectrodes in in vivo rodent experiments are used to estimate viscoelastic parameters of the brain. Using a combination of computational models and experiments, we determined an optimal movement for the microelectrodes with bidirectional displacements of 3:2 ratio between forward and backward displacements and a inter-movement interval of 40 sec for minimizing mechanical stress in the surrounding brain tissue. A regulator with the above optimal bidirectional motion for the microelectrodes in in vivo experiments resulted in significant reduction in the number of microelectrode movements (0.23 movements/min) and longer periods of stable SNR (53% of the time) compared to a regulator using a conventional linear, unidirectional microelectrode movement (with 1.48 movements/min and stable SNR 23% of the time).