Before storage why should a Lithium Polymer battery be charged up to only 40-60%
Actually this recommendation is more for LiIon batteries - LiPo batteries don't seem so much affected by it. The reason I see most times is the self discharge in combination with the protection circuits. The protection circuitry disables the battery when it has been discharged too deep - recovering it from this state is non-ideal for the battery as well as requires a charger capable of trickle-charge preconditioning. To avoid this, the battery should be left in a state that is charged enough.

Also, a constant high charge level shortens the battery life. So its best to charge the battery to an intermediate level only.

Since LiPo batteries don't discharge as much, they are not so much affected by this problem.