This problem damaged my hardwood floors.Ice maker hose leaking. I can not get the copper compression union to firmly stay on supply line. When I turn water on it falls off. I tried to attach two pictures. If this shows up twice, I am still new at this forum.
If this is a new problem with new fitting, could be wrong size. Is the plastic hose coming out of the brass fitting or is the brass fitting coming out of the chrome colored end. The small brass piece should fit snug into the plastic hose. Put the brass cap on the hose first then the small part that inserts into the hose.
Actually, it appears that you have the wrong fitting for a copper tube. The fitting show in the pic is for a poly tube not copper. You need the type of fitting that has a ferrel not an insert.
Here is a video that will walk you thru it ... Wrong fitting is my best guess too: http://www.diynetwork.com/videos/ice-maker-supply-line-leak/14721.html