A robust nonoptical carrier-envelope phase (CEP) locking feedback loop, which utilizes a measurement of the left-right asymmetry in the above-threshold ionization (ATI) of Xe, is implemented, resulting in a significant improvement over the standard slow-loop f-to-2f technique. This technique utilizes the floating average of a real-time, every-single-shot CEP measurement to stabilize the CEP of few-cycle laser pulses generated by a standard Ti:sapphire chirped-pulse amplified laser system using a hollow-core fiber and chirped mirror compression scheme. With this typical commercially available laser system and the stereographic ATI method, we are able to improve short-term (minutes) CEP stability after a hollow-core fiber from 450 to 290 mrad rms and long-term (hours) stability from 480 to 370 mrad rms.