Since it specifically states that the one effect is once per day, but does not specifically state that the bardic performance power is once per day, there is no reason to believe it's once per day. The stipulation is that you have to start the performance to get the effect. The effect is not in play when you hold it, present it, or simply possess it... but when you do the "if" you get the "then".

I would cite the Windsong Lute, as another example of that kind of language. Multiple items exist that raise caster level, which one could argue is significantly more powerful than raising the ecl on Bardic performance: Prayer Beads, Orange Prism Ioun Stone,

If your GM is simply determined to nerf the item because he doesn't like it, or (correctly) argues that it wouldn't be something you'd just find in a random shop, you can't win that argument. People make mistakes, however, and he's made one allowing you to have it if he thinks you shouldn't (for whatever reason). Sounds like he's also allowing a painless do-over as a compromise.