No...magnets remain magnetized because this is a property of how their atoms are oriented internal to the magnet. Magnetism in a normal magnet does not have anything to do with Earth's magnetic field.

However, the shape of the magnet's field can be affected by the properties of the medium in which it sits. In space, this medium is a pure vacuum, and has no effect, however, if the magnet were suspended in a dielectric medium, the shape of its field would be altered by the magnetization of the atoms within the medium.

Return to Ask the Astronomer