Ok so what I gather from stress is that a stress check is only performed the activation phase, never the combat phase. I can't think of any instance where a stress check would occur in the combat phase. Please clarify.

If you were able to perform a free action in the combat phase, you would check for stress. For example if Turr is stressed he can't perform his free actions after an attack.

"Check Pilot Stress" is a specific thing that happens in the Activation phase, because it's linked to your maneuver--it's when you add or remove stress based on the difficulty of the maneuver you executed.

But the effect of stress is always active. If you have a stress token, you can't perform any actions at any time. There are also a number of game elements (for example, Eaden Vrill) that look at whether a ship has a stress token.

Ok so what I gather from stress is that a stress check is only performed the activation phase, never the combat phase. I can't think of any instance where a stress check would occur in the combat phase. Please clarify.

In the original rules, you only checked pilot stress once per turn per ship, right after it did its one normal maneuver.

The newer rules in the Force Awakens core set changed that. You now adjust stress any time a ship executes a green or red maneuver at any time for any reason.

It's rare for that change to matter, though.* Right now, there are only two ship-moving effects that count as maneuvers: Daredevil and SLAM. But Daredevil, by specific FAQ entry, is always white and cannot be changed, so it'll never adjust your stress (at least, not for maneuver reasons), and SLAMming can't be done as a free action, so it can't happen during combat.

There is one example case I can think of where the new rules matter, but it's still in the Activation Phase: use Leia Organa, reveal a red move on your K-wing dial, treat it as white, then SLAM a different red move. The K-wing gains a stress from that second maneuver.

* EDIT: I should say it's rare for that change to matter when it comes to adjusting stress later in the turn. The new rules also make the adjustment happen while you're moving instead of after, which changes how stress interacts with free actions that trigger "after executing a maneuver". That's a separate issue, though.