Maturity effect

Hello,

(1) is straight forward. But can someone explain the (2) sentence for me? Not sure why maturity effect always holds for bonds priced at par, but does not always hold for those priced at a discount. I understand the case of a zero-coupon bond.

(1) '…for the same coupon rate, a longer term bond is more sensitive to changes in the market discount rate than a shorter term bond (the maturity effect).

(2) ‘Note that while the maturity effect always holds for zero‐coupon bonds and for bonds priced at par or premium to par, it does not always hold for long‐term low coupon (but not zero‐coupon) bonds that are trading at a discount.’