Usually the design of mouse buttons, place a pad or rail directly above the switch. That actuator. could be worn, thus requiring a longer stroke on the button to activate the switch.
As Mr. Torus suggests, dirt will also cause activation difficulties.
So, take the case off the mouse, and blow out the switch with some canned air.
Make sure the PC board of the mouse isn't loose, or hasn't slipped further away from the buttons.
Something else you might try, is building up the pad, (or whatever we want to call it), on the bottom of the mouse button with a layer, (or 2), of electrical tape. If that fixes the issue, you could always build up the pad with a very thin piece of plastic glued to the underside of the button, or perhaps a strategically placed drop of epoxy, which you would sand flat after it cures. Whatever you can think of to build the pad up a tiny bit.
With all that said, keep in mind it could be a bad switch, as the law of averages is telling me the left click is used way more than the right, and (arguably), since that side gets the most use, it should fail first. Pay no attention to that rant, as counter-intuitive as it might be to have the right click function is to fail first. After all, stuff happens.