Someone came to me with an analysis of a scale of 16 items, where the Cronbach's alpha computed for that scale was only 0.14. The first thing you should look for in this situation is whether some of the items on the scale are reverse scaled. Sure enough, for 6 of the items, a small value represented a positive outcome and for the remaining 10 items, a large value represented a positive outcome. When the data was recoded so that a large value represented a positive outcome on all 16 items, Cronbach's alpha increased to 0.74.
You can find an earlier version of this page on my original website.