Unfortunately duct tape does not have a very high tensile stregnth. But it would be an inexpensive option!
As with any system, catasprophic failure often has a lot of contributing factors. A weak case is probably a secondary factor really. Gear seperation from shaft flex is probably the main factor in my opinion. Stronger shafts and stronger gears make an immediately noticable difference here. However, seperation between the gears will be greater if the structures that hold the bearings which in turn hold the shafts are allowed to flex.
The concept goes like this: Gear teeth are wedges, and they naturally will try to seperate under load -> This force causes flex in the shafts on which the gears ride. There is a tiny amount of play in any bearing and the shaft will flex until that play is taken up -> At that point the flexing shaft will impart force through the rollers or balls of the bearing into the outer race of the bearing -> If the structure that holds the outer race is not rigid enough to resist this force, the structure will become slightly distorted in shape and the bearing itself will change position with this distortion instead of resisting shaft flex.
By distortion, I'm talking maybe some thousandths of in inch in dimensional change. But that's a lot in terms of change in gear lash. By limiting this distortion, you are limiting the amount of movement in the bearings which in turn is limiting the amount that the shaft is allowed to flex.