You must remember that Dobby is not a Witch or Wizard - he is a House Elf and therefore a different creature. He has a different kind of magic and life source, but because he was seriously injured there was nothing that Hermione - or the trio, Bill or Fleur - could have done for him.
In the book, Hermione had been taken inside Shell Cottage, weak and barely conscious from being tortured with the Cruciatus Curse by Bellatrix. Dobby was critically injured in the chest. In any event, Hermione did not have the healing skills for that type of injury. There is only so much that Essence of Dittany and Skele-Gro, which Fleur had and used on Griphook, will do. The implication in the film version was that the snatchers had confiscated Hermione's beaded bag as one of them said that he had gotten the Sword out of it. So there would have been no access to Dittany. In the book version, of course, Hermione had stuffed the bag in her sock and saved it.