Oh, the woes of enjoying ice cold liquids but hating when your ice melts down and dilutes your flavors. It happens all the time when I'm trying to make my own iced coffee. For some, people try to keep their wine chilled with ice (weird), but this is your next best option -- Simply Chilled Reusable Ice Balls.
The ice balls are pretty simple, they sit in your freezer until ready for use and they have clips that securely attach to your wine glass for minimal movement. Crafted from food grade materials, the ice balls are durable and resistant to staining. They come in a set of 6, which includes 4 large clips, 4 medium clips and 1 ice ball portable unit. ($19.99 @ HomeWetBar)