In this paper we present an investigation into the influence that the chemical structure of a polymer matrix and conditions of its synthesis may exhibit on the durability of a dye being doped in it to aging under the atmospheric, radiation, and other external factors. As a result of this study we have determined an optimal composition of the matrix and identified optimal conditions for its synthesizing. Thus we have found that Rhodamine dyes have better durability in copolymers of fluoroamylmethacrylate than in the copolymers of methylmethacrylate with methacrylic acid.