Yes, give it a haircut & it will rebloom.

Can you provide a photo? These are potentially quite big, tough plants. Is the pot big enough?

I second Cecily's comment. My lawn guy once buzzed my catmint down to 1 inch in July; and it returned later in the summer with blooms just fine, the plants were just shorter, which sometimes can be a good thing.

I have a couple/three catmint/Nepeta planted in full sun the past 5 years and do nothing to them. My lawn guy hasn't buzz-sawed them but they've pretty much tolerated whatever New England can throw at them (i.e., 6 ft. of snow a couple years ago; zero snow this past winter). You state, 'the stalks are not standing tall, but falling over the sides of the pot and the blooms are fading.' My guess would be either some parasite has started chomping on them or they're root-bound in the container(s) and need to be in the ground. In my experience, if the roots are crowded and have nowhere to spread, the plant is going to suffer. Good luck; hope you discover the problem soon.

Not to encourage laziness and sloth, but mine collapse each year and although the neighboring plants do not appreciate being smothered, the catmint quickly sends out new buds along the exposed stems and within two or so weeks there is an entirely new flush of blooms and you can't even tell it fell apart.

I noticed that although the older plants bloom nonstop, container plants which I transplant in the spring will take a short break after blooming before picking right up again. Yours might just be taking a short break.