Hmm.. I just checked and I found an Ultra Ball in the sand north of the terminal (left of the first large area of grass you see). Nonetheless, I think you've probably found another Respawning Item location. Congrats! (The only others I'm aware of are the Berry Forest and Treasure Beach. Could there be more, still?
I'm pretty much sure I've combed the sands of Four Island before.
Edit: Also, in FR/LG, there's no clock, so it'd be measured in either steps taken or play time, not days. I believe these sorts of things are measured in steps.