You can keep saving until you have (close to) enough to either get iruka or upgrade his star. So say if you are at 0 frag 4*, that means save enough for 20x3000=60k points before refining, or perhaps start at 55k since you can only exchange for one set a day, and the remaining 5k will take you the 20 days or so.

This way, if a new breakthrough is released in the mean time that you would use, you can get that.
If not, it doesn't really affect the time at which you get iruka so you don't really lose out.
This will effectively delay the time at which you get the seal/summon scroll, but those aren't all that important.