Safety aside, there is no reason to expect damage from leaving it up, unless of course it leaks down and damages part of your shed. ON subject but slightly getting off is the story of my fuel tank leaking.
When my fuel tank cracked and I thought I may have to get it hauled to the dealer, I left the FEL up for 4 weeks. It did leak down about half way in that period. No one here but me and the wife and she doesn't go near the tractors. I left it up so if we needed to load it on a trailer we could without cranking it since the tank was leaking dry. Finally after 4 weeks, I took the tank off and put JB Weld on the cracked out bolt area which stopped the leaks. About 2 weeks later my new tank came in. This was almost 2 years ago and the old tank is still installed and new one is in my shop taking up space waiting for the old one to start leaking. The hydraulic valves on the LS are amazingly leak proof. I have left the 3PH up for 3 months at a time with a heavy disk on and absolutely no leak down. And as stated above the FEL lowered very slowly. The valves on my Kubota backhoe all leak down even overnight I can see movement of the bucket, boom and dipper, even the stabilizers leak when in full up. But I am getting off topic again.