I can't answer your question as to refrigerating gelatine solution as I don't do it this way but once Colloidal Silver is capped, it can sit out on the table or counter forever as long as its in a sealed container (mason jar or similar). It will NOT go bad and I've had some lying around for several years at this point and its still fine.
I don't actually make enough Colloidal Silver often enough to justify making pre-dissolved (bloomed) gelatine solution. I just sprinkle what is needed on the surface of the finished Colloidal Silver slowly so it sinks and blooms without causing clumps which would never go into solution, let it sit a while, give it a stir with a chopstick (wooden - its NOT "cold" and as such won't pick up any of the gelatine), cap and let cool.