Origin
'Common sense' in a philosophical context has often been used contrastively. For instance, Claude Buffier (1661-1737), oppposed common sense to Cartesian scepticism, or what passed for such since Descartes was not a sceptic.
Bishop Berkeley (1685-1753) opposed common sense to the manifest nonsense, as he saw it, of material substance.
A fully-fledged defence of common sense dates from the Scottish School of the 18th century : take Thomas Reid's An Inquiry into the Human MInd on the Principles of Common Sense (1764). Reid influenced both Dugald Stewart (1753-1828) and Sir William Hamilton (1788-1856).
Btw Aristotle does recognise 'common sense' when he takes into consideration, as in the Nicomachean Ethics and elsewhere, 'ta endoxa' - widely held beliefs. He is seldom willing to ignore these, even if he rejects them or refines them out of all recognition.
Response to query
Speaking of Aristotle, how did he use 'phronesis' and how did he relate it to 'ta endoxa'?
D.J. Allan can help here. 'How did Aristotle use 'phronesis' ?
The central figure ... is the man (sic) of practical wisdom (phronesis) in whom habitual rightness of desire is combined with habitual truth of judgement, and who is equally competent in formulating general rules of action and in applying them to the swiftly changing situations of life, in such a way as to do justice to all concerned. It is the intuitive judgement of such a man which serves as the criterion of right action for all who do not yet feel confident of their own power of decision. Not that by his judgement he can make actions right or wrong. He is, to some extent, simply a faithful interpreter of prevailing moral standards, who can point out what society would demand in the given case. (D.J. Allan, The Philosophy of Aristotle, Oxford: OUP, 1970: 133.)
'Prevailing moral standards' are not seen as merely conventional; Aristotle is no moral relativist. He has a teleological view of the world in which the moral life of the polis or city-state is appropriate to human nature.
Now for ta endoxa.
Ordinary moral thinking, which ta endoxa represent, is the range of recognised or received opinions. It generally contains a kernel of truth, even the essence of a matter, but it does not necessarily articulate the exact moral truth:
But again - and this side of the picture ought not to be ignored - he [the phronomos, the practically wise man: GT] has considered these standards more carefully than the average man; he can justify them by a philosophical view of man's place in the universe, and perhaps in some rare cases propose to modify them. (D.J. Allan: 133.)
Persistence
The philosophy of mind, or philosophical psychology, is a test case. There is a split approach. On the one hand, writers such as Donald Davidson and Jennifer Hornsby work within the tradition of common sense or 'folk' psychology, conceptualising with a great deal of sophistication ideas of action, intention, weakness of will and the general run of concepts which we use to interpret the mental life of ourselves and others. (But justice cannot be done to Davidson in a few words.) On the other hand, philosophers such as Stephen Stitch and the Churchlands regard folk psychology as pre-scientific and they foresee the wholesale replacement of such psychology with one that correlates or identifies psychological states and events with neurophysiological ones, and generates a new vocabulary for the mind - one in which the concept of the 'mind' itself is unlikely to survive as too tainted with folk or common sense psychology.