Fish. When do they stop sensing something is amiss?

[synesthetic]

There comes a point when fish sense "something is amiss" no matter where you try to go, no matter how far you try to move. If anyone else has noticed this, would you happen to know when it resets?

I've been going after Titanic Sawfish for the past few days (obviously with no luck) and have been achieving the above state after.. I don't know.. somewhere well over 500 crab balls, I think? When it first happened to me, I just put the game down and found something else to do; I figured that it'd reset at JP midnight. This time, I've been fishing through the night and early morning, then at around 7:10am PST (just past JP midnight) I'm hit by the above situation again.

And I like fishing at Parata's Peace just next door for my peiste maps. So I'm concerned that I'm locked out of fishing for my map for the day. I could go BTN at the Bramble Patch for it when I go to do my beastman dailies later, but I'd still like to know when does this fishing lockout reset for future reference.
Because I gotta catch 'em all, and I'm sure I'll run into this issue again.