While there are some that still believe that Left 4 Dead 3 will happen, most of the fans believe that the game has already been killed off and that Valve has no intention of making a third sequel.
If one needed more proof about the end of the franchise, maybe this will convince them. It was been reported that Erik Wolpaw, one of the co-writer for Left 4 Dead has left Valve. With him gone, the chances of Left 4 Dead 3 happening is even slimmer now.
Erik Wolpaw also had a hand in the Portal and Half-Life franchise which is why it is not looking too good for both those games as well. While Valve has not made it very clear, most people believe that Valve is done creating games like this and that they are more focus on some of the bigger multiplayer online game that they have now.