It's kind of hard to wimp out by conceding a race you lost.
Exactly. Conceding also doesn't change anything. If they suddenly find a few thousand extra votes for Burns, he wins. In the very unlikely event that happens, Burns would serve the next term, and Tester could not cry that Burns has already conceded and try to get sworn in even though Burns was certified as wining the race. Refusing to concede at this point just makes you look like Al Gore.
And yes, weird things do happen. About a decade ago in San Antonio, a judicial race was reversed when the votes were canvassed a week after the election. Either two precincts had not been added to the totals, or they had been added twice, and the error was not discovered for a week. The original "winner" had received a concession, and was on a cruise ship, when he got the word that he didn't win after all.