I don't like the magic repair kit, a major immersion killer for me. I think some added realism can add variety, drama and more realistic outcomes. Some good ideas on here.
Something like in the Silent hunter games would be quite good.
-crew can be assigned to repairing
-Priority of repairs can be chosen
-Some damage can not be repaired or fully repaired at sea.
-An estimated time of repair is given
Could combine that with what some have said about carrying spare parts
-Some spare parts could be needed and consumed for repair, if those parts were realistically carried