Absolutely you can still successfully flip houses even in a down market. You need to set your goals at a higher profit before you buy, so you will have a larger cushion in case the market continues downward. You might not make as much money as you originally expected, but you will not get hurt, either, if you plan your flip correctly.
Remember, in a depressed or downward trending market, many people still buy houses. There are buyers out there. As far as sellers go, many people will not be able to afford necessary repairs before selling their houses, giving you many opportunities for bargain purchases. Other sellers are facing foreclosure or similar matters that motivate them to sell cheaply.
Also, as more and more people face foreclosure or sell their homes to get out from under heavy mortgage payments, those same people must move somewhere else. Typically, they move put a tenant in place, and then sell that rental house to an investor. Many people who lose or sell their homes do so, not because they could no longer afford the monthly payments, but because they got behind on their payments for some temporary problem and then cannot afford to catch up again. Those people are willing and able to pay relatively high rental rates, sometimes for the same home they used to own.