In general, a dealership cannot repossess your car if you fail to pay the down payment within the agreed-upon 30 days. This is because the dealership does not have a security interest in the car until you have fully paid for it. However, the dealership may take other actions to collect the down payment, such as sending you a demand letter or filing a lawsuit.
If you are unable to pay the down payment, you should contact the dealership and explain your situation. They may be willing to work with you to come up with a payment plan. If they are not willing to work with you, you may want to consider hiring a lawyer to help you negotiate a settlement.