Later in the series, Peter visits Syler to learn his ability, but Peter comes into contact with Syler on multiple occassions in the first season, but never picked up his ability. Is there something different about how Syler works that prevented Peter from picking it up?
The key to Peter's ability is that he must be empathetic to the person in order to access their ability. Hence the powers name of Empathic Mimicry
Seeing as Peter never had anything in common with Sylar and actually rued his existence, he could never be empathetic with him enough to absorb his ability.
It wasn't until Peter was desperate enough to need Sylar's Intuitive Aptitude to understand a solution to his current situation. He then obtained it from a different version of Sylar from a different timeline, one that had grown softer due to his connection with the child and helped explain to Peter what this ability truly can do.
On Peter's wiki page on the Heroes Wiki, you can see that he comes in contact with all kinds of abilities but never displayed them.