Lexan is the way to go. It is also known in the manufacturing industry as polycarbonate sheet. At my day job it's what I make machine guarding panels from.
You can actually order it as mirror, and I do believe it is cheaper than glass mirrors, however I am going by what I was told. I have never priced glass mirrors in 4 x 8 sheets. http://www.curbellplastics.com/ is where I get ALOT of my plastic materials from. Making a mirror maze that is impact resistant, you should use at least 1/4" thick mirrored Lexan and frame it real well.