Trifecta

It appears that in his Enquiry concerning Human Understanding, Hume uses three main arguments to defend his skeptical approach to epistimology. These arguments are used at different times to supplement and build upon eachother, not circumvent flaws.
The first argument states that all ideas must come from impressions, and all experiences are, themselves, impressions. Simple ideas are copies of impressions and complex ideas are manipulations of two or more simply ideas. There are no ideas which do not come directly from impressions, and the recollection of any idea is, in that moment, an impression itself.
His next argument focuses on an inability to make predictions. This is predicated on the idea that predictions aren't true by their definition, demonstrative, or based in any other relation of ideas. Because it is conceivable that a prediction can be wrong without being contradictory, it does not stand the test of Hume's limited use of reason.
Finally, the third and perhaps most controversial argument outlines an inability to find an idea for necessary connection. Building on the first two arguments, Hume claims necessary connection is impossible to directly experience, making it impossible to have a true idea of its nature. This impossibility along with its noncontradictory nature, make causality unknowable.
These three arguments all lead to the same skeptical conclusion and feed off one another rather than fill the gaps the others leave, as has been suggested.