Puzzled by wet weather issue

So...2003 4.8L, automatic, stock. 209,000 miles. In normal driving, most days, no issue, have driven a few hundred miles in a day without a problem.

But, about a month ago, I went through a puddle, deep one. Car didn't turn off, never misbehaved that evening.

However, now, if the weather is like today, rainy, wet, and cool (about 50F), it will start right up, drive for a bit (let's say 15 minutes) and then, if you come to an idle, it might just turn off. Starts right back up easily, but it...

Puzzled by wet weather issue