Neural-network-based adaptive dynamic models are commonly used to estimate allowable control travel and the proximity to a limiting flight condition in the design of advanced envelope protection algorithms for fly-by-wire aircraft. In this paper, linear models are compensated with adaptive neural networks, which use instantaneous sensor data as well as past flight history information for concurrent learning. A law for collecting appropriate training data into the history stack is established. It is observed that using the proposed time history data for online neural network training provides more accurate dynamic trim and control limit predictions compared to using instantaneous sensor data only. Simulation results for a fixed-wing aircraft during maneuvers show comparisons between the different adaptation schemes.