I checked the records and since the major-leagues expanded to thirty teams with the addition of the Rays and D-backs in 1998, a total of 37 teams have started off the season going 1-5. The table below lists them all, ordered by year, and gives their final record as well. Teams in bold made the post-season; teams in italics are those who, like Arizona this year, played all six of those games at "home" - don't forget, for scheduling purposes, that's how the two contests in Australia are considered. The table is sortable by clicking on the column headers.
It is obviously way too early to give up on the Diamondbacks. The poster child for a poor start not necessarily being a season killer was right here in Phoenix. It was 1999, where the team started off exactly as this year's model did, losing five of their first six games, and were only at .500 on May 4, with a 14-14 record. That team exploded late in the year, playing .750 ball (51-17) down the stretch, and ending with 100 wins, setting a franchise record that has never been matched since. However, they started the season in Los Angeles and Atlanta, not at home, and as we'll see, that makes a difference.
Overall, however, you have to say the numbers above are not exactly encouraging. Of those 37 teams to begin with one victory in six attempts, only four made the post-season that year, though things are now a little easier than they were there, with the addition of a second wild-card. But even reaching the .500 mark for the entire season was accomplished by a mere eight - as well as the 1999 D-backs, the 2003 incarnation of the team also managed it, [The Philadelphia Phillies appear the masters of the false start: they went 1-5 three times, in 2004, 2006 and 2007, but still finished above .500 every time]
So, while it's still possible to have a good year, we should not be under any illusions as to the difficulty of the task ahead for Arizona. Because the bottom line is, more often than not, teams that start off this badly just don't recover. The mean number of wins put up over all these cases was 73 (so, going 72-84 the rest of the way) and the median was 72. Things get even darker if we focus in on the eleven italicized sides, who like the 2013 Diamondbacks, played all of those first six games at "home". None of them made the playoffs, and the 2006 Phillies were the sole franchise to finish above .500, going 45-30 after the break. The average record for those eleven sides? 69-93.
Let's hope the 2014 Diamondbacks aren't one of those, and there's no denying, every team is different. I certainly don't think this team is as bad as the 2012 Cubs or last year's Astros. But I will feel a great deal better about going forward, after they have put some more wins under their belts, and ideally, swept the Colorado Rockies at Coors this weekend.