This card says: "battle: choose your performing unbowed monk and target an enemy personality or follower: Give it -3F. If it has no attachments and you have played two or more other Pierce the Tapestry this battle, destroy it. If this did not destroy it, you may take an additional battle action to play a Pierce the Tapestry." My understanding is that this needs to have been the third Pierce the tapestry you play in a battle for you to be able to take the additional battle action as it states if this did not destroy it meaning the third Pierce the tapestry. Not meaning you can take additional battle actions to chain the first three in a row.
Pierce the Tapestry
A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
See that conditional effects are worded as follows: IF <condition> THEN <effect>.
You have two conditional effects, one dependent upon the other. But the conditions are always checked, even if they return <false>. If you haven't played two other copies of Pierce the Tapestry, the condition is checked, it returns <false> and therefore the destruction effect doesn't occur. Therefore, "this" (the first conditional effect) hasn't destroyed it, so the condition for the second effect returns <true>, and you get the additional action. Only when Pierce the Tapestry destroys something will the second condition return <false>.
You may take the additional action no matter how many copies of Pierce the Tapestry you have played, as long as the destruction effect fails or is prevented. The reason the destruction didn't happen is irrelevant, the destruction's condition is always checked.