I have made some form of pickled eggs by hard-boiling them, peeling them, and dropping them into lacto-fermented pickle brine after the pickles are gone. I've left them at room temp for several days, but that's all I have personal experience with.
I looked here:
http://cooking.stackexchange.com/questi ... rigeration for some answers, including some people who keep them for several months in brine, but you'd need to balance that against this:
http://www.cdc.gov/mmwr/preview/mmwrhtml/mm4934a2.htmThough I would hasten to note that that CDC article is a single case, specifying that they'd never seen that happen before. So it must be extremely rare. My personal take-away is not to puncture the eggs in an attempt to get the brine at the interior.