Two-dimensional covalent organic frameworks (2D COFs) are periodic, permanently porous, and lightweight solids that are polymerized from topologically designed monomers. The predictable design and structural modularity of these materials make them promising candidates for applications including catalysis, environmental remediation, chemical separations, and organic electronics, many of which will require stability to mechanical and thermal stress. Based on their reinforced structures and high degradation temperatures, as determined by thermal gravimetric analysis (TGA), many reports have claimed that COFs have excellent thermal stability. However, their stability to heat and pressure has not been probed using methods that report on structural changes rather than the loss of volatile compounds. Here, we explore two structurally analogous 2D COFs with different polymerization chemistries using in operando X-ray diffraction (XRD), which demonstrates the loss of crystallinity at lower temperatures than the degradation temperatures measured by TGA. Density functional theory calculations suggest that an asymmetric buckling of the COF lattice is responsible for the observed loss of crystallinity. In addition to their thermal stability, XRD of the 2D COFs under gas pressures up to 100 bar showed no loss in crystallinity or structural changes, indicating that these materials are robust to mechanical stress by applied pressure. We expect that these results will encourage further exploration of COF stability as a function of framework design and isolated form, which will guide the design of frameworks that withstand demanding application-relevant conditions.