Free Ascended after HoT is repeatable?

Hi guys,

I started working on Ascended Gear, I already bought all the LW3 Ascended Trinkets/Backpack (It was a bit tedious but pretty easy), got my Elite Spec Ascended Main Weapon (Since I use a PoF Elite Spec it was very easy) and I got lucky on some PvP Reward and I already have two Ascended Armor Pieces.

As secondary Weapons I use two Swords, and I know that you can obtain an Ascended one after you complete the Story of HoT (From what I heard is easier to obtain than normal), but after I do obtain it with a Character, if I complete again the Story with another one can I obtain a second Weapon? Or it is a one-time Achievement?