Ok so my Carvin Bolt T, which is without a doubt my favorite guitar, doesn't seem to hold tuning for very long. Now it has a trem on it, but I have locking tuners on it. But even when i'm not using the trem, it seems to go out of tune kind of easily. I've pretty much decided that it could be either the strings or the nut. The strings haven't been changed since late January, but it does have a graphite nut on it.

So how could this problem be solved?