Each time rotten flesh is caught, it causes the mod to stop working, with the rod just bobbing up and never reeling in.

To my knowledge there is no behavior in vanilla Minecraft that would cause this to happen. The mod only detects when the bobber moves in such a way that signifies a catch; there is no awareness of any loot drops. More than likely you are playing on a server with a plugin that attempts to detect AFK fishing. Typically these plugins will stop giving catches after a certain amount of time until you move the player or the camera.

OP may be referring to the actual bobber-head catching on loose entities floating in the water, such as dropped items (and villagers stuck within your fishing waters), which I have also experienced causing the same issue - no more sounds/movment, no more autofishing.

I'd investigate, but I have University exams right now.

same, i always have this problem. My temporary solution is to reduce the chunk, graphic etc to the lowest possible and it somehow extend the time before crashing about 20 to 50% idk how things work anyway