Adam Funk wrote:
I have a couple of Ikea, wall- and ceiling-mounted, fluorescent
lights, each of which has a curved, thin plywood cover with a lot of
slots in it, lined by a sheet of diffusing white plastic. The lights
are good except that after a few years the plastic linings are
deteriorating and falling apart.

Thats Ikea for you..

Can anyone recommend a type or source of flexible plastic suitable for
replacing them?

Not that wont suffer the same fate.

Replace with something that is fit for purpose.