Plexiglas is a trade name for acrylic. It shouldn't "turn brown" for generations. What does discolor is styrene which is sometimes sold as a cheap picture framing substitute. Nor does it outgas like vinyl. It would take a lot of UV to spoil it within any reasonable period of time. What does happen is that acrylic can warp (bow) due to temperature or humidity issues. It is not permanent in the sense that glass is, but neither is any kind of photographic medium ever invented. Even glass is not utterly permanent. It hydrates enough to spall off its surface every few thousand years. But someone might break it next week anyway. "Archival" is a relative term; and in this respect, the main advantage of glass would be its reliable flatness. But there are also kinds of coated acrylics and crystalline plastics like polycarbonate you could also experiment with.