So if I hold the strings down with my left hand (I'm right handed), shouldn't they resonate more? It feels like it goes away so quickly.
I am using a classical guitar (3 metal strings, 3 nylon), and I am pushing down the strings, as far as I can, till they touch the neck.
No. As long as you're already fretting the strings firmly enough that the contact with the frets is good, holding them down more firmly won't make a significant difference to the sustain. The most audible result of pushing them all the way down to the fingerboard will be to push the note slightly sharp due to the increased string tension.
@topo morto gave a great technical explanation.
I would like to add:
I highly recommend that you go visit your nearest guitar store and try a variety of guitars. You might find that either your strings are old, guitar body is damaged, your neck needs a setup, or you simply don't like the way classical guitar sounds. You'll find out by trying out what resonates more for you.
My very first guitar was a $12 classical guitar from a yard sale that I received as a gift. I do remember asking myself why the guitar wasn't resonant enough, but I think that was because I was influenced by electric guitars and acoustic guitars on youtube and on albums, I expected the same sound on this guitar. Nowadays, I go back to this guitar appreciating the way it sounds.
Also remember that a lot of guitars you hear in the media are mic'd, so they will sound different than how you hear it against your body.
I hope that helps!
