You should not stop trying to do the short sale. Were you working with a realtor? Either way, you need to find one who is familiar with short sales and hire them right away. Look for the SFR (Short sale and foreclosure resource) or the CDPE (certified distressed property expert) designations. You also need to look your home up on http://www.makinghomeaffordable.gov to see if you qualify for a HAFA short sale.
I can't imagine why a bank would turn down a short sale offer unless it was unacceptably low. Many times homeowners are appraoched by 'investors' who are involved in some very questionable practices. The banks will NOT work with these people, however, if the home is listed with a realtor, and reasonable offers are presented and negotiated in good faith, the banks are usually pretty reasonable.
Once the short sale is completed, you will need to find a home to rent, your real estate agent should be able to help you with that as well. We are here to advocate for our clients, whether it is for a sale of a rental. Let us help you.