Improve survivability of bicycle container The "white container box" lasted about 2 months until it cracked in multiple places.

It was a cheap box(Dollar General variety).

New container is made by Sterilite and much sturdier.

I believe the old container cracked because of vibration and bumps transmitted from the ground to the box.

Can someone help me with ideas on how to cushion the new box?
The traditional solution on bicycles is metal wire basket. Metal is tougher than plastic and mesh instead of sheet metal makes it lightweight enough. 

If you need something waterproof, put your things in waterproof bag or get a more expensive bike-specific rack box.