The main reason for not re-using oil is a health issue...cooking oil at high heat changes its molecular makeup.  Each successive time it is used it becomes more and more a "saturated" fat, even tho you started out with unsaturated corn or conola oil.
Olive oil is only slightly less likely to burn than butter when used for frying.
A non-stick pan by its nature requires very little oil.  I am not a fried fish gourmet but cannot see how deep frying the fish would make it taste different from using a non-stick pan and just a little oil.  Depending on what is used for breading, deep frying may be necessary to keep the coating from sticking to the pan.  Again, a non-stick pan would solve that problem.