For heaven’s sake, why didn’t somebody teach how to spell and punctuate this expression to some writers? Probably because it’s one of those rules in flux.
Most writers learned that any time a possessive is used, an apostrophe is needed. As the expression shows that sake belongs to convenience, it ought to be spelled/punctuated for convenience’s sake, right?
Not exactly. The use of sake allows for two exceptions to the above rule. First, if the word coming before sake ends in an ss, most speakers would find it difficult to say aloud, and it sure would look darn ugly on the page or screen, so the ’s is dropped. Hence, we write for goodness sake and not for goodness’s sake. Secondly, if the word coming before sake is more than a couple of syllables long and ends in ce, most speakers likewise find it awkward to say and so the ’s is dispensed with. Hence, we write for convenience sake. In all other cases – such as for Pete’s sake or for God’s sake – include the ’s.
Of course, not all speakers (and therefore readers) find adding that ’s particularly difficult to say. So they say it. And then some authors write it. Ultimately, this is one of those grammatical rules in flux, and increasingly dictionaries and grammar guidebooks are allowing for either spelling/punctuation as acceptable, standard English.
As a writer, you can avoid the matter by revising the phrase to for the sake of convenience. Otherwise, stick to the original rule of no ’s or whatever the style guide of your publishing house advises.