Back in 2012, the MBTA funded a project to improve the drainage. The project was executed sometime in early 2013 - I can't find a reference to exactly when, but it resulted in the two new sheds that you can see on the west end of track 1. Here are two articles:
MBTA to improve drainage at Natick station (8/20/2012)
T preparing to start station drainage improvements in Natick (12/29/2012)
The problem is that the Natick Center is depressed 'beneath' downtown Natick. The only drainage from the station is to the northwest towards Lake Cochituate. And there isn't much of a slope (at least initially) away from the station.
On Friday morning, 8/21/2015, sometime between 7 AM and 7:29 AM, Natick got slammed with a huge downpour. Dave Epstein in South Natick reported 1.51 inches of rain in the storm. I'm saying after 7 AM, since P582 made it through without any trouble (apparently), and P582 should be passing through on track 2 about 7 AM.
When P506 arrived close to it's scheduled arrival time of 7:29 AM on track 2, the track was flooded. Here are two pictures just before P506 arrived (click on the Read More):