We prove that the flux function of the totally asymmetric simple exclusion process (TASEP) with site-disorder exhibits a plateau for sufficiently dilute disorder. The result is established under a decay assumption of the maximum current in finite boxes, which is implied in particular by a sufficiently slow power tail assumption on the disorder distribution near its minimum. To circumvent the absence of explicit invariant measures, we use a renormalization procedure and some ideas inspired by homogenization. MSC: 60K35, 60K37, 82C22