I'm going to share my recent experience with a disclaimer that we've used ME every single trip and not had any issues until this one.
We arrived around 2:30 PM and had two checked bags tagged for ME. We went straight to Disney Springs after we got off the ME bus and returned to our room around 9:00 PM. Only one of the checked bags was in our room. I figured that our airline had lost the 2nd bag and called Bell Services to find out how I should proceed. To my surprise, Bell Services confirmed my bag was not lost (yay!) but instead on-site and being "processed". They said that sometimes ME bags are delivered at different times. Ok, fine. It took another hour and another phone call before someone finally showed up to my room with the 2nd bag.
This was nearly 8 hours after we landed. Point in case, in my personal experiences, these issues are rare, but it was a good reminder that delays can and do happen, and if you absolutely need something out of a checked bag, you may be better retrieving that luggage yourself before boarding the bus, or bringing those items in your carry on.