For this question you're on the right sub-forum. As for training-sessions I'm not 100% sure but lets say you open a map in Surveyor, place a train of choice on the track and save that session - you can run that session from the start over and over. However a save within the session that ends up in "saved sessions" is unreliable IMO. It appears some information is lost. This is because it saves at certain points and not necessary exactly where you saved. The result can differ, industries, popups not working and cars not loading. Is it a glitch? Yes I think so. I always make my own sessions and always run them from start.
Lets say you're shooting from the hip because this works for some who won't agree to the above. Try saving at different points and maybe you can pick the session up at a later time.