This is definitely a problem as I see it as well. I don't think inventing a new way to use repair kits will fix it though. Personally I'd prefer if repairs required resources; for example:
You can buy extra spars, cloth, oakum, planks, etc. at port.1
The resources you have on board limits the amount of repairs you can do at sea.
When sailing on the open sea you can instantly repair your ship using these resources (and limited by them).2
When sailing in a battle instance you have to be on survival mode to repair, and the repairs take time.3
1 Spars should be hard to come by in large quantities, and all resources should be limited by ship size.
2 For example, you can only repair your sails if you have the sailcloth, only replace masts (preferably only minor masts, topmasts, etc.) if you have the spars, and only repair your hull if you have planks and oakum, etc.
3 Alternatively the system could be revamped entirely; something like this.