The Rays demoted Beckham to Triple-A on Wednesday after he committed his third base-path gaffe of the team's six-game road trip.
His latest miscue cost Tampa Bay a run on what became an 8-6 loss to the Boston Red Sox.
With the Rays leading 4-1 in the fourth inning and Beckham already on second base, Kevin Kiermaier hit a ball to right-center. Beckham should have easily scored but failed to hustle home, and when Kiermaier was thrown out trying to stretch the hit into a double, Beckham's run was ruled to not count as he didn't cross home plate prior to Kiermaier being thrown out.
Though manager Kevin Cash said both players were at fault, Cash put a greater onus on Beckham's blunder.
"Definitely the not hustling," Cash said was worse. "That is required of us, and that's probably the easiest part to do in baseball."
Beckham declined to comment, according to a team spokesman.
Beckham's previous two strikes against him occurred while the team was in Houston. On Saturday, he got caught between bases on an infield single. On Sunday, he also failed to hustle home, but that run counted.
The 26-year-old Beckham is batting .247 with five home runs and 16 RBIs in 63 games for the last-place Rays.