If one assumes quantum physics and the whole space-time disfiguration thing (a.k.a. real life Time Kompression), you could feasably have days pass without advancing in time. I just have no idea how it would be measured or how it would even be noticed.
For explanation, consider this example. A sheet of paper is our universe. We can move around in it by moving up and down the line. However, the paper is also moving, unbeknownst to us, through time. If the motion of the paper was unobservable to us, how would we know if it stopped?
We've seen that moving at such high speeds increases gravity and slows time, so by moving fast enough, we could be moving only through space and not time. Trouble is, in order for space-time difiguration to occur, you'd have to be moving damn fast. Like, so-fast-you-and-everything-around-you-would-die fast. Fast enough such that not a thing in the known universe could propel you at that speed. Oh well.
I would prefer to be known as BlackWaltzTheThird, or just Waltz for short. Happily married to Hilda/Hilbert's MILF as of June 4th 2012.