It sounds like someone has used the wrong solvent / cleaner on the surface. Plexiglas / perspex should not be affected by sunlight per se, although it is possible that a subsequent UV coating is degrading. Or just that the surface is contaminated with oil / grease that is reacting with sunlight.
From a datasheet:
plexiglas is a trade name for acrylic plastic.
Characteristics of the material
- Acrylic Plastic
- Half the weight of glass
- Impact resistant
- Unaffected by sun or salt spray
- Temperature range of -30 to 160° F for continuous service
Cleaning:
Wash with mild soap or detergent, with plenty of lukewarm water, dry with soft cloth or chamois.
Grease, oil or tar can be removed with hexane or kerosene. Solvent residue should be removed by washing immediately.
Do Not Use window cleaning sprays, scouring compounds, acetone, gasoline, benzene, carbon tetrachloride or lacquer thinner.
Plexiglas can be sanded and polished - but test on an inconspicuous area first! There are lots of resources on the web for how to go about sanding and polishing.
SD