the Doctor's still on the case. Remember, though, that what he's now trying to do is fill in the gaps. They did find her in "Let's Kill Hitler" -- or rather she found them, somewhat to their confusion.
By the way: The question ought to be "Have they given up ..."
Also remember that a few of the latest episodes were actually supposed to have taken place before we knew that River Song was Melody Pond. So their lack of concern about her may simply come down to that.
In fact, until "A Good Man Goes to War", they'd no idea they had a daughter to be looking for. I believe "Night Terrors", at least, was originally intended to be broadcast before they (or we) knew Amy really was pregnant.