For those having problems with intonation (which means being able to hear pitch differences), it is indeed possible to train the ears to be absolutely infallible.
That may indeed take some time and effort on the part of the individual, but these days we have so many wonderful tools that allow for us to work on our own (not visit and pay a live teacher, for example), and use of softwares for ear training can greatly accelerate the process. I know this from teaching my own students.
Band in a Box has the Ear Trainer inside, which is something that used to take at least two people to do back when I was a freshman in music school. It is *excellent* for Interval Recognition, Chord Recognition, both of which develop the Relative Pitch sensibilities, and it can also be used for pitch identification, such that one can develop the Absolute Pitch ability if they so desire as well. Ten to Twenty minutes a day with the Ear Trainer is all it takes and it is just like playing a Computer Game.
Then there's the Tuner.exe program inside your bb folder, as previously mentioned in another thread here.
The only students I've ever encountered who could not improve these abilities were those who started out with the basic statement that they could not do it. That is a self-fulfilling prophecy, the only reward from such being the chance to say, "See, I told you I couldn't!" -- Attitude is 90% of the process.
--Mac