Clue: Sex and the City — it has one staying up (6)
Answer: VIAGRA
Explanation: Definition: it has one staying up
 VI(Roman numeral for "six", represented by the English prefix "sex-", as in "sexcentenary") **plus**(*and*) AGRA(the city in N. India – where many go to see one of man's – or one man's – greatest erection for a favourite wife).
Defn: …, ie. that which lets one stay up/erect.