In addition to the most excellent comments above, I'd also suggest that part of the vibe is the subtle interplay between how the parts are played, not just in the timing, but in the accents, the dynamics, the ebb & flow of intensity, the passion, etc. You can play the same part with exactly the same timing, and give it a different feel with just some subtle differences. Sometimes it seems that this vibe can be lost when repeatedly re-recording parts to get that perfect take.
Coming back with fresh ears can help to clear the cobwebs. I think of a studio owner I once knew who used to teach recording engineering classes out of his studio. He used to tell his students that one of the important roles of the Producer was to occasionally interrupt the artist to say, "Dude! It's just not happening!" While he said this to amuse himself, there's a certain amount of truth in it. Sometimes, when we are struggling unsuccessfully to nail that perfect take, we need to stop and do something else for awhile. Let the brain reset. Give the voice/hands/fingers/etc. a rest and come back to it later.
I also think that it is sometimes helpful to try different variations on a theme with some tracks. Try playing that drum part really hammering that snare and kick. Try it again with a lighter touch. Track it with and without extraneous fills. Play a simple bass line. Try nailing those accents hard. Take another pass with a little popping and slapping. Lock the bass in with the drums, then play off of the drum part.
This is probably very obvious to everyone else, but I've found it helpful to try playing with a different feel, even if I know I'm probably going to scrap those tracks. Sometimes, those minor feel differences can spark a whole new vibe that I end up liking better than my original vision for the song.