Learning and remembering the basic techniques of a piece is something that takes practice. Most of the pieces I have memorized aren't always in the perfect state they were when I last performed them, but after a few hours with the score--preferably spread over the course a day or a few days-- the piece will be ready again. This might even be away from the piano. Developing and nurturing your musicality helps a lot too since as you play you can hear your interpretation; the musical aspects will come more naturally from the notes as you practice playing this way.
Memorizing many pieces or even long works also takes a lot of practice. One thing about memorizing is to not rely on muscle memory. Don't let the piece just "play itself" unconsciously. Memory slips will happen and you'll lose the piece easily. Muscle memory isn't as evil as some might say, but you want to develop other types of more cerebral memory. Looking at what chords you're playing in a piece, visualizing the score, any type of theory relationships you can find all help! After a while, you'll see all these similarities within a piece (that the composer probably had in mind) and even similarities between different pieces. Grouping passages into patterns helps.
Think about the A chord for example. You know the A tritone is actually three notes, but if I tell you the A chord you know exactly what I'm talking about. Mentally group the piece so that you can think of a passage as one whole in the same way as the A chord (three parts) can be thought of as one. The concept is fairly simple, but it takes a lot of practice. The basic idea is start with the small pieces and get bigger. Start with a passage at a time and as you master a passage, you can then master a few passages and then combine them into a pieces then more and more into a repertoire. Don't try to learn the hardest possible pieces. Those can be worked with with your teacher each week. Instead, learn pieces below what you'd consider your difficulty level. You'll learn them much easier and faster; since they aren't as hard, your mastery of the notes will make it easier to concentrate on musicality.