Superconducting qubit lifetimes must be both long and stable to provide an adequate foundation for quantum computing. This stability is imperiled by two-level systems (TLSs), currently a dominant loss mechanism, which exhibit slow spectral dynamics that destabilize qubit lifetimes on hour time scales. Stability is also threatened at millisecond time scales, where ionizing radiation has recently been found to cause bursts of correlated multiqubit decays, complicating quantum error correction. Here, we study both ionizing radiation and TLS dynamics on a 27-qubit processor, repurposing the standard transmon qubits as sensors of both radiation impacts and TLS dynamics. Unlike prior literature, we observe resilience of the qubit lifetimes to the transient quasiparticles generated by the impact of radiation. However, we also observe a new interaction between these two processes, "TLS scrambling,"in which a radiation impact causes multiple TLSs to jump in frequency, which we suggest is due to the same charge rearrangement sensed by qubits near a radiation impact. As TLS scrambling brings TLSs out of or into resonance with the qubit, the lifetime of the qubit increases or decreases. Our findings thus identify radiation as a new contribution to fluctuations in qubit lifetimes, with implications for efforts to characterize and improve device stability.