Jamie65: I'd like to say "Yes, those worn parts would definitely see more frequency." but it could be dependent on heat on the action (expansion), or whatever??? Let's discuss this some more.
It's hard to diagnose over the Internet without actually seeing this occur in action.
Because you mentioned that you are using very light loads, some/many of the Perazzi guys with 12 gauge guns who use tube inserts for the smaller gauges like 28 and 410 experience that a similar scenario. What happens with these is that there is just not enough "kick"/recoil to force the Inertia Block (as I call it), Perazzi calls it #158, "Connector" back far enough to get it unhooked, for lack of a better verb. The reduced recoil does not slam the "Connector" back and away from the sear it has just tripped. In this case then, the Connector does not return to battery under the second sear. Their solution is to install a meatier Inertia Block and Perazzi sells them and I carry them.
In your case with the MX3 (I shoot an MX6 better than the other models) shoots top first, so the left sear is the one you are having trouble with. It just could be that the Connector is not "unhooking" from the left sear and when you cock the gun, the Connector and sear mating is not letting the hammer "catch" the front end of the sear to stay cocked. If the stock was off you could see this happen.
If your problem was with a second shot as in doubles, then the Connector issue I just mentioned above would be more prevalent. However, as I understand it, you fire your gun successfully, open the action to eject the spent hull, reload, close and then get failure-to-fire. This just has to be in the cocking mechanism, or even too tight of a stock bolt, or the above Connector issue.
Have you removed and reinstalled the stock lately? If not, dismiss this possibility.
Could even possibly be that some wood in the tang area is rubbing on the side of the left hammer... I am guessing, but picking my brain for possibilities. As I stated, it would be nice if when this happened, you could immediately stop, remove the butt-stock and inspect the trigger area. Even a failing ejector rod on the left side could be involved, but unlikely.
Sorry this is so long, but I am trying to cover all possibilities. It's hard to describe brain surgery over the phone, so to speak. Give me a call if this condition persists and we can talk more about it. I am sure you want it fixed ASAP, as we are in the shooting season.