I think Time Turners can only be used to go back in time for a certain amount of hours, not days and definitely not years. Harry might not have been able to travel back far enough. Also, there's the risk of accidentally making things worse by changing the past, and the risk of being seen or killed in the past. And remember, the Time Turners were all effectively destroyed in Order Of The Phoenix.
Felix Felicis is hard to brew, and probably expensive too. Slughorn also said that overusing it can lead to bad effects.
