  Correlated insulators are frequently observed in magic angle twisted bilayer
graphene at even fillings of electrons or holes per moir\'e unit-cell. Whereas
theory predicts these insulators to be intervalley coherent excitonic phases,
the measured gaps are routinely much smaller than theoretical estimates. We
explore the effects of random strain variations on the intervalley coherent
phase, which have a pair-breaking effect analogous to magnetic disorder in
superconductors. We find that the spectral gap may be strongly suppressed by
strain disorder, or vanish altogether, even as intervalley coherence is
maintained. We discuss predicted features of the tunneling density of states,
show that the activation gap measured in transport experiments corresponds to
the diminished gap, and thus offer a solution for the apparent discrepancy
between the theoretical and experimental gaps.
