What you describe is pretty much exactly what has been happening with my i3 Mk3 the past few weeks, but since I'm so new to 3D printing I've been having a difficult time problem solving this particular issue. It ran extremely well for the first two months (I ordered and assembled it in December) and printed some incredibly beautiful models with no failures. Suddenly about a week ago after updating to the newest firmware I began having trouble with the printer losing home and beginning calibrations around the middle to back left corners and subsequently "crashing" or grinding to a halt when the bed moves too far forward. When trying to move the bed manually from the screen I am only able to move is slightly in a single direction. For example, even though the bed is centered it can only move forwards not backwards, since the bed location is registering as 0. Additionally, the bed was getting way too hot and prints were peeling as well as a few other odd issues that hadn't happened before.
At first I assumed it was corrupted firmware, so I reverted to 3.5.1 but all the issues still kept happening (even if I didn't manually stop the print), so I did a factory reset and re-calibrated. Just to do my due diligence I also checked and tightened the belts which are now at near perfect/recommended tension (although I tend to have a lot of stretching in the X belt fairly often). As recommended by others above, doing a self test usually fixes the issue, but not always, so I'm not entirely sure whether its a hardware or software issue at this point.
I ordered the new mk3S printed parts so instead of dismantling everything now, I'm hoping that installing these and trying the firmware update again might solve some issues. I'll update after but any help or insight/advice in the meantime is so appreciated