I had this happen when my level 10 fisher turned elderly status, which disappointed me, because I had planned to have him retire and fish for deathfish in the indoor pond I had stocked for him (Angler and Hates Outdoors - dang random legacy traits).
For me the problem resolved itself one day after work (science lab), when he started fishing automatically in the pond behind the lab.
Maybe if you try changing to work clothing or putting them in a situation where they might fish unprompted it may fix itself. I dunno, but I know that resetting the sim didn't work for me.
I think my sim was unable to fish for 3ish days...hard to tell, though.
-Two