Laying down shouldn't have bothered them very much, though that may be a symptom of too little sun. I would have waited to cut them back until new growth showed at the base, but in your climate that shouldn't have been a problem either. Buut...since you cut them back, why do they have any stems showing anyway? Normally, when you cut back a Gaillardia, you cut it to the ground.

I would also look for differences: is it on a slope while the others are on the flat? Does it get less food than the others? Does it get less or more water than the others? Is the soil different? Does it get less sun than the others? All these factors can affect the growth and health of it.

One other thing to consider is if the label was correct. 3-4 ft. is mighty big for this variety, but about right for varieties of G. pulchella with similar blooms. That species may survive your winters, but, next spring,it will still look like it wished it could die!

Kevin : )

Either they weren't labeled correctly or didn't get enough light. "Arizona Sun" is known to be a compact version of Gaillardia, less than 12". They may have exhausted themselves, they usually aren't an extremely long bloomer. And you do usually cut them back after you see new growth. Perhaps you got a bad batch of plants?
Sorry I can't offer better advice. Better luck this year!