Predicting out-of-sample solutions is challenging for projection-based reduced-order models (PROMs). In practice, the number of solution snapshots is severely limited by the high computational cost of the full-order model (FOM), and if the predicted solution is far from the training snapshots, the reduced dynamics may drift away from the high-fidelity trajectory and the error can grow rapidly in time. As a result, an additional difficulty for constructing accurate PROMs with limited data is to detect during the online stage when the PROM is no longer reliable and to recover accuracy without sacrificing the computational benefit. This talk presents an adaptive, time-local hybrid FOM/PROM strategy that aims to combine the computational efficiency of the PROM with the accuracy and robustness of the FOM. The key idea is to run the PROM whenever it is sufficiently accurate and to switch locally in time to the FOM when reduced predictions degrade. The switching decision is driven by an error estimator consisting of an additional PROM for the error. In contrast to indicators that rely on local error accumulation, the proposed estimator integrates the error dynamics in time, yielding accurate estimates and enabling reliable detection of loss of accuracy. Moreover, the PROM includes an adaptive enrichment mechanism: when the estimated error exceeds a prescribed tolerance, the FOM is temporarily activated and the resulting high-fidelity solutions are used to update the PROM, improving subsequent predictions. The performance of the proposed approach is evaluated on transport-dominated flows, including shocks, governed by the compressible Euler equations (e.g., two-dimensional NACA0012 airfoil). The results demonstrate accurate and robust out-of-sample predictions with a significant reduction in computational cost.