I have a 3-hole Kohler toilet. Every once in a while it leaks from the bolts... I've finally figured out that this happens after I remove the top or nudge the tank in any way. Then it drips slowly. For -months- I thought it was leaking from the base.

I now realise that if I shake the tank it somehow 're-aligns' it and then it stops leaking. Until the next time the tank gets bumped.

Do I need to replace the screws/gasket with the entire 'kit'... or is there some way to re-align it so that it stays properly sealed?

Like I said, after it stops leaking it stays dry as a bone... sometimes for months at a time... until it next gets bumped.