Thanks for the replies, guys.
A little BUMP for an update...

The original Acu-rite I had continued to die over the next several days after posting. The display continued to change at will and eventually, the numbers began to fade. Changing the battery did nothing. I contacted the Amazon seller, who promptly send me a replacement unit for free. By the time the new unit arrived, the original one was barely readable. I also noticed with the new one next to the old one, both units displayed different temps, and the old unit was jumping around wildly at that point (e.g., going from 89F to 114F to 125F, etc.). I just assumed the original unit was defective, tossed it in the trash, and moved on.

Of course, as of this morning, I find the newer unit is starting to display the same behavior...jumping over to display the clock for no reason.
Did I possibly receive not one, but TWO, defective Acu-rites?!?
And if not, what the hell am I doing wrong here to break them?

The unit sits inside the enclosure on the cool side, attached to the wall with velcro. I don't move it at all. Humidity is generally between 50-80%.
People generally speak very highly of these units, but I'm not having any luck with them at all.