A picture would sure help, you did a good job describing it, tho. Those hinges are not cheap. Can you add some vertical pieces either inside or outside to tie the slats on the back of the bin together at the hinges? Maybe too heavy of hinges? when you are lifting or closing do you put extra pressure on the hinges,working against the hinge restraint causing the hinge to exert a twisting force to the top rail? Will the lid close by itself if it is left alone to do so, if not you have too strong hinges. A size lighter hinge might help.
Herb
Herb