The current Tigers swoon unfortunately reminds me of the final weeks of the 1967 season, during which they repeatedly refused to take advantage of opportunity after opportunity to seal the deal. This is from SI right after the Red Sox clinched:
"The Tigers kept lurching into contention and then, as though aghast at finding themselves in the spotlight, scurrying into shadow. They beat the White Sox twice, once with a spellbinding seven-run rally in the ninth, then dropped a doubleheader the next day. They rallied to win four straight and the lead, then bowed 5-0 to the Washington Senators and blew two seemingly sure wins to Boston. They rallied again to win three straight, then threw away a 4-2 lead to Washington in the ninth. On the final weekend of the season, confronted with successive doubleheaders, they won the big first game each day and then died in the second."
In some ways, this season is worse, since they've been in first place for a much larger portion of the season than the '67 team. But the end result is in danger of being the same: wilting under pressure, while another team thrives.