AAs still confuse me a bit with how all the tables connect together, but I believe this will do what you want.
The effect is just a spell, so if you want to change that you need to edit the spell. It's id 6886.
To change the reuse time you need to edit two places in the database.
Code:
UPDATE altadv_vars SET spell_refresh = (5*60) WHERE skill_id = 1377;
UPDATE aa_actions SET reuse_time = (5*60) WHERE aaid = 1377;
Replace 5 with however many minutes you want the reuse time to be.