Whether you must continue making payments on your wife's vehicle after she announces that she's leaving you depends on a variety of factors, namely whether the vehicle is your wife's separate property and when it was acquired. If the car is owned by both of you, you are both responsible for the car payments until the court awards the car and responsibility for payments to one of you during the divorce.
Date of Separation
Until you and your spouse are divorced, both of you are responsible for marital debts. These are typically debts acquired during the marriage including a car loan, even if the vehicle title is placed in only one spouse's name or only one spouse drives the vehicle. Depending on the state in which you live, the date your wife announces that she is divorcing you may be the official date of your separation. Usually, spouses only remain jointly liable for debts acquired between the date of marriage and date of separation. However, this may not be of much help if the car was purchased and car loan payments began during your marriage.
Separate versus Marital Property
Regardless of the state in which you live, property, including debts, is characterized as either separate or marital property based on when the property was acquired. Generally, separate property is property you obtained before the marriage or during the marriage by inheritance or gift. Marital property, on the other hand, is property either spouse while married. During the divorce, the court will distinguish between the two types of property. Typically, separate property remains with the spouse who owns it and marital property is divided between the two spouses. If your wife's car was acquired prior to the marriage, purchased with separate funds or she received it by gift or inheritance, the court is likely to award the car to her and hold her responsible for making payments on the vehicle after the divorce is finalized. If the car was purchased during the marriage, the court could award it to either of you -- and usually the spouse awarded the car is also given responsibility for making payments.
Payments on Separate Property
If the vehicle is your wife's separate property, you are not responsible for making payments on the auto loan, either during your marriage or after your wife tells you that she wants a divorce. As for any payments you already made, the court may treat these payments as gifts to your spouse, unless you can prove that the payments were not gifts; for example, by providing the court with a written agreement between you and your wife stating such. However, if the vehicle's character as separate property was changed to marital property during the marriage, both you and your spouse remain responsible for the payments until the court assigns responsibility for the debt. This can happen if your wife placed the title in both your names after you two were married. Similarly, if the car was always marital property, both of you are still responsible for payments until the divorce is final and court assigns responsibility.
Affect of Divorce Decree on Auto Loan
Regardless of what your divorce decree says, the bank will go after whoever signed the auto loan. If both you and your spouse signed for the car loan, the bank can legally go after both of you for payment. If only you signed for the auto loan, but the court awarded the car to your wife along with responsibility for payments, the bank can still come after you if your ex-wife fails to keep up with the payments. For this reason, it is advisable to have the title changed into your wife's name if she is awarded the car, as well as refinance the auto loan into just her name if your name is on the loan.