I can tell you exactly why you are having this problem. This cover needs to be removed to perform routine oil and filter changes. For whatever reason, Lesus uses very small washers to secure the shroud.
Careless removal and replacement causes some of the threads to become stripped and some are overtightened. Others are just plain not replaced (because who ever looks under their car) figuring if 9 or 10 bolts is good, 5 will do it okay. I had my local Lexus dealer leave mine off completely when the did an oil change I specifically told them I did not want.
This rough treatment o the underbody shroud, not to mention the forgotten mounting screws or bolts (10mm) that hold it on soon causes it to fail.
You must remember that there is a great deal of air prssure under the car so there is quite a bit of force on the mounting bolts. Without this cover your alternator will take on water which will not cause immediate failure but will limit the longentivity.
I would repair it with fiberglas cloth and resin, kind of a messy job but very do-able. Glue it together good with JB Weld first. Go to a hardware store and buy some large washers and place them as the final contact against the shroud plastic. You will be good to go.