When should I change the cleaning solution in the contact lens case?

Daily. For chemical disinfection - the solution should be changed daily and the case allowed to dry. For hydrogen peroxide systems, the lenses can sit safely unopened in the case for about a week. Longer than that repeat the sterilization cycle.
Every day. The cleaning solution can become contaminated if left in the case too long, and at the very least, it may not be as effective over time. You should replace the contact lens cleaning solution daily in order to minimize the risk of infection.