Fuses don't always go imediately. If you have a 20 amp fuse (as an example) and suddenly put 20.1 amps through it, it most likely wont blow, at least not quickly. It may even continue to hold even at 21 or 22 amps for some time, but the higher the amperage, the faster it will blow. So you may have a short, but not a strong one, so it's only drawing slightly over the amperage of your fuse, allowing you to run for a little while, before the fuse element heats up and melts/burns, thus cutting the connection.