Higher-order groups, formed through interactions beyond pairwise connections, are essential for the resilience of many complex systems. Prevailing hypernetwork resilience models that address functional group failure rely on two limiting assumptions: either a single node failure triggers group-wide collapse, or the group remains functional with at least one surviving node. While useful as conceptual limits, these models oversimplify the progressive loss of structural integrity in real systems. Here, we propose a tolerance-based framework for hypernetwork resilience that describes a structural disintegration process driven by cumulative node failures, where a hyperedge becomes nonfunctional only when the fraction of its failed nodes equals or exceeds a tunable tolerance threshold c. This approach naturally unifies the two classical limiting cases into a single continuous framework. We develop a theoretical framework based on the message-passing approach and validate its accuracy through extensive Monte Carlo simulations on synthetic homogeneous and heterogeneous hypernetworks. Our results reveal that the tolerance threshold c acts as a decisive control parameter: increasing c significantly improves system resilience by lowering the percolation threshold, whereas low c exacerbates fragility. Furthermore, application of our model to diverse empirical networks—from political committees to commercial activities—demonstrates a robust framework for quantifying complex system stability