Sure it can. The AP set trim to maintain your AP settings. When you provide a small but steady input, i.e. you pull the yoke slightly the whole time, AP is moving trim further to compensate your input. That is going further and further and at a certain point, AP loses control and disengage and then you’re done, because trim is at the very end. Maybe I’m wrong but you can check by yourself. Take a look at the trim settings when it happens.
I just read your initial post again, and if it’s not the flightmodel I’m quite sure that there is something wrong with your controllers.