The obvious way to prevent the mortgage on the second home from negatively affecting your credit rating is for you to continue making your monthly mortgage payments in a timely manner. You mention in your question that you are current on the mortgage on the second home, so you should continue making your payments to keep the mortgage current, if possible. In the meantime, you can either look for another tenant to rent the property or put the home one the market. If you can find a new tenant, his or her rent payments should help you cover the mortgage payments. If you prefer to sell the home, you can hopefully sell the home for enough money to cover your current mortgage and also make a bit of a profit on the sale; selling the home will free you from the mortgage obligation altogether.
Since the housing market is in a slump, selling the home may be the best option. Selling now will allow you to cash out your equity before the value of the home decreases any more, and will free you from the worries of owning a home that is losing value by the day. In addition, it will relieve you of the hassle of maintaining the property, paying property taxes, and dealing with tenants. Before you decide either to continue renting the property or to sell it, I encourage you to consult with a professional financial advisor in your area to help you determine the best course of action for your situation. You will need to carefully analyze market trends to determine if you stand to gain or lose by continuing to rent the property, and if selling is a feasible option given current market conditions. Generally speaking, when the housing market slumps, rents tend to increase, so continuing to rent the property may be a feasible option if you think that housing prices will rebound in the near future, allowing you to continue building equity in the home.
Basically, the determination of whether or not to sell the home is too complicated for me to address in a short answer. You will need to discuss your situation with financial consultants and real estate professionals in your area to determine the best course of action in your situation.
To learn more about mortgages, I encourage you to visit the Bills.com Mortgage page at http://www.bills.com/mortgage/. In addition, the Bills.com Credit page, available at http://www.bills.com/credit/, offers a wealth of information relating to credit, credit reports, and credit scoring.
I hope that the information I have provided helps you resolve your financial difficulties and helps you Find. Learn. Save.