in which a German team mentioned someone examining the surfaces of medical silicone objects disinfected with H2O2 and concluded that there was no damage: "Treated and untreated samples of silicone and polyurethane tubings were studied by scanning electron microscopy (AMR 1200; Fa. Leitz, Wetzlar, Germany). The surface was smooth; no cracks or surface alterations were found as a potential indicator of damage."
They simply wiped with H202, so I don't know about soaking, and I know that some people have expressed concerns, but this seems to at least indicate that it's not going to destroy your cup. I haven't had any problems with peroxide so far and it's one of the safer disinfectants out there, but will update if I run into problems.
Meanwhile, here's another page that rates silicone as having "excellent" compatibility with H202 at concentrations of 10%, which is at least more than 3 times what would be used for disinfecting.