The word "fuck" in the expression, "Oh, for fuck's sake", is not an instance of the act being committed, but a generic form describing the spirit of the expletive. There are multiple postings on the Internet about the incredibly rich variety of parts of speech filled by the word "fuck". This particular form is one of the rarer variants, describing the general sense of impatient antagonism precipitated by competence being boondoggled or thwarted by stupidity.

As every intelligent being has experienced, trying to get something done, or solved, when countered by the popular elements of stupidity (including its subclasses bureaucracy and pigheadedness), produces a collision of energy waves in the mind which then explodes, leaving the beleaguered individual in the state of mind referred to by the expletive "FUCK!".

That one four-letter word thus is imbued with an immense cargo of analysis, planning, hope, frustration, indignation, exhortation, expostulation, and perjorative stoicism. It is in celebration and acknowledgement of this most useful of terms that the expression, "Oh, for fuck's sake" has come into widespread acceptance.