On the piano the notes just fade away and have to be replaced by new notes!
This is especially tough on your worst hand - which for almost all human beings is the left one! "But Dan," I hear you object! "I'm left-handed! Shouldn't it be easier for me?" Answer me quickly - how often are you forced to use your RIGHT hand? Which hand do you trust the most to accomplish a task? When I ask those questions of lefties, they all look sheepish and tell me they trust their RIGHT hands - because they have to. The machinery of our society is designed for the Right-Handed person. Even a piano!
Think about it - ages ago, most folks were righties. The melody of any tune is formed by the highest pitches in it. That's cause higher pitches are easier for humans to hear. Thus, they (the Power that Be!) combined these three important parts of any tune - the melody, the higher pitches, and the need to be right-handed and made keyboards so they go higher to the right rather than the left.
Still, the foundation of the house of music is NOT melody but rather rhythm. Guess which hand forms the "rhythm driver" of the piano! Hint: it ain't the Right Hand! Music without rhythm does not move forward, even in a European tune. The left hand, your worst hand (for reasons I already gave) drives the music you play - or not!
Sorry, but that's the way it is. I'd wager you're like the hundreds and hundreds of students I've had of every age and your left hand works poorly. In fact, the nicest thing you can say to a pianist is, "You have a great LEFT hand!" Try it and you'll see.
Got other troubles learning to play? Maybe I can help. I'd like to help but not being able to read your mind, I don't know how to help you. Email me. I promise to respond and pretty quickly!