I don't know what it is about March, but that's when A.V. Club's Mike D'Angelo and The Conversation's Bruce Isaacs each independently posted great analyses of Eternal Sunshine's closing scenes.

Here's D'Angelo:

When I first pitched Scenic Routes, back in the summer of 2009, one of my big selling points was the idea’s sheer inexhaustibility. Over the past seven and a half years, I’ve analyzed 175 scenes, yet barely scratched the medium’s surface[...]

“I should finish by writing about one of the great movie endings,” I immediately thought, and just as quickly, I knew exactly which one it should be.

[...]It’s never been clear to me whether Kaufman views these two characters as admirably quixotic or ludicrously self-deluded. Maybe it’s a bit of both. Director Michel Gondry repeats the final image of Joel and Clementine running in the snow, creating a loop. (This isn’t in the screenplay, which just ends on Clementine’s “Okay”—the most baller move I’ve ever seen in script form.) That suggests an infinite repetition of the same mistakes, though the implied pessimism is offset by Beck singing “Everybody’s Gotta Learn Sometime” on the soundtrack. Regardless of what was intended, I can’t help but perceive these lovers’ renewal of vows, so to speak, as intensely romantic—and not exclusively in the lovey-dovey sense. Maybe it resonates less strongly for those who believe in an afterlife. (Source)

And here's the Isaac piece, which comes with the video posted below:

The film is about memory, desire, love and loss. In this scene, Isaacs focuses on what he calls two “cinematic gestures” in the closing sequences of the film.

The scene features Joel Barish (played by Jim Carey) and Clementine Kruczynski (brilliantly portrayed by Kate Winslet) as they realise their relationship is doomed but still worth pursuing.

It is, says Isaacs, a beautiful and deceptive sequence that includes one of Jim Carey’s finest moments on screen. (Source)

 

Bonus: couple of weeks ago, the Medium Jump podcast had a look at Eternal Sunshine. 

Additional information