Regarding the second player, is he an upcoming restricted free agent? If that's the case, he may have broken off negotiations but the game is still allowing you to enter offers so you can make a qualifying offer despite negotiations having stopped. He won't accept them (regardless of how good the offer is) until he's ready to begin negotiations again, which will look like he's rejecting the new offer but he's actually just in a state where he won't consider anything.
For the first one, could you upload the save (
instructions here)? I'd like to have a look at it, the negotiations normally shouldn't affect morale for anywhere near that length of time.