Lithium-ion batteries are well-known to be plagued by a gradual loss of capacity and power which occur regardless of use and can be limiting factors in the development of emerging energy technologies. Here we show that separator deformation in response to mechanical stimuli that arise under normal operation and storage conditions, such as external stresses on the battery stack or electrode expansion associated with lithium insertion/deinsertion, leads to increased internal resistance and significant capacity fade. We find this mechanically induced capacity fade to be a result of viscoelastic creep in the electrochemically inactive separator which reduces ion transport via a pore closure mechanism. By applying compressive stress on the battery structure we are able to accelerate aging studies and identify this unexpected, but important and fundamental link between mechanical properties and electrochemical performance. Furthermore, by making simple modifications to the electrode structure or separator properties, these effects can be mitigated, providing a pathway for improved battery performance.