As you asked me, sadly, i have no idea of your issue. did you copy as you said or migrated? If this is a copy maybe the copied blueprint can’t find the references to the linked output (which seems to be your hud) and maybe only a migrate will solve this. Try to create a new project and migrate your blueprint to see if it happens too.
I did a short hunt in docs and answerhub and found only those two troubles which could be related : Blueprint pins are always disconnected when project is opened - UE4 AnswerHub and Blueprint loses connection every time editor restarts - UE4 AnswerHub
First one is really old but as your doonce goes to possibly a hud, there maybe have a function reference issue. (or timeline)
second one seems to be a glitch after migration 4.4 to 4.5 ( is that your situation ?) and has for origin the case of your functions / blueprints. try set names with lowercases characters and see if it happens again.
If nothings solve this, try to redo this blueprint in a new 4.5 project (yes i am sure you will not want to do this one because of the amount of work, but if you are really in need to no more have to link this wires on copy / migration…)
Those are only ideas and i am sorry to no more can help you. If after all of that, you’re always in trouble, and absolutely need to have those links not disconnected, best way seems to post in answerhub :https://answers.unrealengine.com/index.html