I'm not quite shure if this is myth, superstition, or pure sillyness but it seems to work for me. (20 fishing, 2million gil on selling moat carps... during the christmas inflation

, and 400/10,000 on my own Lu Shang's)
If you notice that it takes longer between casts or that you're catching really stupidly low amounts, just move. Move like 10 feet. There is suposed to be a creeping loss of fishing prowess as you stand still. Again, that could be goofy. Every little bit helps though.
I found that the "Hard Fatigue" limit comes at about 200 casts... which turns out to be around two stacks of materials for making Insect Paste (24 stacks of paste). The only thing to do is wait. This also seems to be around 4-5 hours if you're fishing in Port Sandy. Thats just from long boring experience.... long... boring... *gurgle*. If I hadn't sold them and used them for the quest... I'd only be at 1,600/10,000. Thats another story. I'd also not have leveled crafting.