Is a comma after the word introduced by 'let alone' in the middle of a sentence needed?

Solution 1:

The second comma is mandatory.

It is difficult for the decision-makers to believe, let alone accept, that the increased hardware-security would outweigh the production loss caused by security-enhancing measures.

"Let alone accept" is parenthetical in your sentence, i.e. it's an extra piece of information which is not essential in order for the sentence to make sense -- if you remove it, you still have a perfectly correct sentence. Parenthesis is set off by a pair of punctuation marks which can be two commas, two dashes, or two brackets.

Dictionary reference has a more detatiled definition for parenthesis:

Grammar. a qualifying, explanatory, or appositive word, phrase, clause, or sentence that interrupts a syntactic construction without otherwise affecting it, having often a characteristic intonation and indicated in writing by commas, parentheses, or dashes, as in William Smith—you must know him—is coming tonight.