I have the Bigfoot levelers and the company says it is okay to store the jacks up or down since the shafts are stainless steel and don't rust. I always spray them well with a silicone spray as per manufacturer's recommendations.
Our hydraulic cylinders do not rust. We have been full-time since 2011 and sit from 4-6 months at any one time with the jacks down/extended. We have been within a mile of salt water and that didn't happen. This is not true. I would say, consult your owners manual or see if there is an answer on your manufacturers website.
If they are hydraulic cylinders (can you see a shiny shaft extended when they are lowered?) then they should be stored in the closed/retracted position. Otherwise, rust will form on the shaft, and when retracted after storage, will damage the hydraulic seals.