You can certainly store 'em full... I've often had a tank go months between fill and use just because I didn't need that tank for a dive.
However, tanks, especially aluminum, should be stored either full or nearly empty (200-300 psi) as a fire safety precaution. Here's why... if exposed to fire, a full tank will blow the burst disk before the tank heats up to the point that the aluminum is dangerously weakened by the heat, while even a tank weakened by the heat can take the pressure likely to be reached in a tank that starts out with only 200-300 psi in it.
A tank with some intermediate pressure in it, however, may not blow the burst disk, but may have enough pressure in it to cause a catastrophic failure of the tank should the tank temperature get high enough to weaken the aluminum. The guys trying to put out the fire would not be amused.
Rick