If a man petitions freemasonry and is “blackballed” can they reapply or is it a one shot deal?

With 50 different states, and 51 Grand Lodges, the regulations and by-laws vary widely. Normally, an individual petitions a lodge, and the lodge will appoint a committee, to examine the individual’s fitness for Masonry.  If there is some reason that the individual does not make the grade, it will normally be discovered in the investigation.  If the report of the committee is favorable, then the lodge will proceed to vote on the candidate, and the vote must be unanimous.

If the candidate is rejected, (in some jurisdictions) he may re-apply. Masonry believes (among other things) in assisting good men in becoming better. The bar is high. Candidates can be rejected for a felony conviction, substance abuse, moral turpitude, atheism, etc. I encourage any man who is considering Masonry, to discuss the standards with the lodge secretary. If he feels confident of making the grade, then I would encourage him to press on with his application.

Although I understand you are not writing from Massachusetts, but Japan (where we actually have a lodge, by the way), to answer your question, a applicant who is denied admission to a lodge does have the opportunity to reapply. There are some guidelines that need to be followed.
-Robert