Nope. It stays connected. Use it once and that's it. It doesn't charge again.
That's what i'm doing. Time always runs out on the last few.
I'll try again tonight but it's not working for me. Having to turn the cannon around while firing the missiles and then pressing R1 gets very awkward.
EDIT-
To be more clear. I use the winch after all the question marks are lit up.
I think I know what the problem is. You can't hit all those targets on the end right? Play the main story a bit more.
Also, you don't have to hold R1, one press is enough.