Some higher order mode (HOM) passbands in multicell SRF accelerating structures may become “flat,” meaning that they have an extremely narrow bandwidth due to weak coupling between cells. In the presence of random perturbations caused by mechanical imperfections of the cell shapes, such passbands can split into individual cell resonances that are weakly coupled or completely uncoupled from the beam pipes. As a result, these modes can exhibit high quality factors and large R/Q values, potentially leading to beam instabilities, emittance growth, and excessive cryogenic losses. This effect was observed in a high-beta 5-cell 650 MHz (HB650) prototype cavity developed for the PIP-II project. An analytical theory explaining the origin of this phenomenon, along with methods to mitigate it, is presented in this paper. The HB650 cavity was successfully redesigned to eliminate the flat HOM passband and prevent the associated detrimental effects.