Evidently this was caused by age and perhaps sunlight wearing out the plastic. First one door handle (passenger side) lost all tension and then driver's side a month or two later. I will say it's a bit embarrassing climbing into a car from the trunk, but since the CR-Z has that open trunk situation it's not awful and I'm a small, limber guy.

The process of replacing the door handles was made easier by a fellow and his father doing it on Youtube, step-by-step so that was nice. What wasn't nice is that I had three bolts that were completely seized up, destroyed, and had to be drilled out. Honda seemed to alternate between cheapo plastic that would break and invincible depleted uranium armor.

Ultimately, two of those bolts were extracted out with screw extractors, while the final required sawing through the head of the bolt to get out (with only a dremel, it took a while). If not for those bolts the whole operation could have been handled in a couple of hours no problem. I bought new ones (for fear that used parts would wear out and I'd be in the same situation again).