Real estate purchases involving multiple offers can be tricky and create delays for buyers such as yourself. The results from the appraisal should should be available within several days. Also there could possible be other reasons for a deal falling apart....inspections can create serious problems as well.
Our recommendation is to move forward with your search, leaving your offer in place, but remaining current and exploring other options. If you find something that appeals to you, you can then present a letter of "cancellation" withdrawing your offer from consideration prior to submitting a formal offer.
Being the back up offer really benifits the seller because you are essentially an insurance policy that they can fall back on it the first deal fall through....you on the other hand, are stuck playing the waiting game...with in most cases, nothing to show for it.....move forward and keep looking!