Connie is definitely the protagonist, and we know that because she's the only one who changes over the course of the novel. It's tempting to think that Mellors is a secret protagonist but, let's be honest, he's more of an Author Avatar. Only Connie has any kind of character arc, even if it's only from "bored" to "adulteress."
To be fair, she does struggle ("agon," Greek for "struggle" or "competition"). She struggles against Clifford; she struggles against her marriage; she struggles against the soul-crushing coal-mining town (is there any other kind?) of Tevershall; and she struggles against society. She even succeeds—kind of.
Although she manages to find a lover who cures her of her ennui, she doesn't actually escape Clifford or Wragby. Her most impressive act is conceiving a child—not much heroism there. In fact, it's something that even sixteen-year-olds with questionable parenting skills can handle.