Amazingly enough (since we were just speaking about this) this paper just appeared http://iopscience.iop.org/0953-2048/27/8/082001/pdf/0953-2048_27_8_082001.pd... "A trapped field of 17.6T in melt-processed, bulk Gd-Ba-Cu-O reinforced with shrink-fit steel" Superconductor Science and Technology 27 (2014) 082001 (5 pages). They have a golf-ball sized ball of GdBa2Cu3O7 superconductor surrounded by a cylinder of shrunk-on stainless steel for strength. They placed it, while warm, in the bore of an 18T electromagnet, cooled it to 26 kelvin, then gradually turned off the external field over about 1 day long turn-off time. Result: 17.6 Tesla of "trapped field." If warmed up to 50 kelvin, it still trapped 10 Tesla. If the "pinning" of the "flux tubes" by crystal defects had been perfect then this trapped field would have lasted forever at 26 kelvin. However, in fact, it gradually leaked away, falling to 17.4 Tesla after about 200 minutes. This is because the flux tubes were occasionally able to move because the pinning was not infinitely strong, hence migrated out of the superconductor and were lost. If a neutron star were a type-I superconductor, no magnetic field would be possible inside. If type-II then you could have flux tubes passing thru like in this experiment. However, I would expect, due to the claimed superfluid nature of neutron star stuff (i.e. not a crystal with defects), that the flux tubes would be mobile, in which case they, like in this experiment, would be expelled. However, I would guess the time scale for the expulsion would be seconds at most, not (as here) about 1 week. But this is just a guess. If the neutron star really were a crystal with defects, then the crucial question would be the pseudo-energy barrier that a flux tube would have to surmount to move from one path-of-defects to another, and whether that barrier was much larger than the thermal energy. (It perhaps also could quantum tunnel thru the barrier, an option which is of negligible importance for lab-accessible superconductors, but perhaps would not be negligible for neutron star stuff.) Trying to understand that purely by theory without experiment, seems to me very difficult and I would not believe anybody who claimed (as of year 2014) to be able to do it.