Are you just targeting it and running up to it with your weapon drawn? If so, that's not enough to initiate the attack. Observe the target icon on the mob when you start your approach. Is it a circle icon? Or is it three daggers pointed inwardly at the mob? You're not actually "engaged" unless you see the three daggers. Otherwise, you're just standing around a mob Only when those daggers are present will you begin auto attack.

The reason why you AA after using a skill is because using a skill automatically engages you with the mob. At least it should. It has been that way in my experience. Generally, the way to engage a mob is to draw your weapon, target it, and then hit your confirm button on your joypad or the enter button on your keyboard from what I can imagine. The problem is there's not much much of a audio or visual cue other than the silent switching of the cursor icon. It's not very noticeable, while drawing out your weapon makes you feel like you're engaged to fight. Try hitting the confirm button or enter key until you start attacking.