I want to get the golden fishing rod. The wiki says I need to complete 50 quests.
Does your progress end when the angler dies, or does it carry on with the amount of quests you completed with the previous angler?
The Angler quests progress by a counter attached to your player data, not based on the actual Angler person. I have jumped worlds and completed quests in multiple worlds on the same character to advance my quest queue.
From the wiki:The Angler - Notes...(second to last note)
The Quest completed count is character specific, meaning you are able to accrue the number of quests required for an item given as a reward, from completing them on multiple worlds.
So if the Angler dies, your progress is still valid and will continue when the next Angler shows up.