I've noticed a similar problem with my two-way player (SP/C), so I decided to try a Starting Pitcher to compare perk progress, and here's what I've noticed:
The description for hitting perks says "... drive in runs, move the runner over, and rack up clutch hits...", which seems to be pretty straightforward. I have the difficulty cranked way down, so these happen a lot.
The description for pitching perks says "...strike out batters, hit your spots, and keep the scoreboard clean..." With the difficulty set very low, I 'seem' to do this a lot with my two-way player, but perks aren't unlocking. With my SP, however, I started to notice "high leverage outs/strikeouts", and have unlocked a few perks shortly after getting a few of these. The "high leverage" situations I've seen so far are:
7th inning, game tied at zero, runner on base, final out
8th inning, game tied at zero, bases empty, first out
9th inning, game tied at zero, bases empty, first and last out
extra innings, game tied at zero, runner on second, first and last out
With my SP, these occasionally happen because the offense gives me no run support, but with my two-way player, they never happen - because we are never tied (or losing) in the 7th inning or later when I am both pitching and in the batting order.
The Fielding perk description says "... highlight-reel catches and flawless plays...", but my SP unlocked one during a routine groundout where he wasn't involved in the play, and another striking out the batter for the second out in the third inning, so I don't know what's going on there.
I haven't really tested out the Baserunning perks, so I have no insight to offer for that.
I hope an upcoming patch will improve this.