I just picked up one of these and was doing some research on the timing of it and found this in a post:
In December 1915 Joseph Fahys (BWCCo) passed away and was buried in Sag Harbor. In 1928 the factory was closed and production ceased, due to a disagreement among Fahys heirs who did not want to invest in the company and upgrade equipment to compete with foreign watchcase-manufacturing competition, particularly the Swiss. A key competitor was an Austrian watchmaker named Joseph Bulova. In 1937 a group of Sag Harbor citizens formed the Sag Harbor Guild and approached Arde Bulova, son of Joseph Bulova from Bulova Watch Co., to reopen the factory. The second floor of the factory was leased to Bulova Watch Co. managed by Arde Bulova. During World War II the factory had almost 500 employees manufacturing items supporting the war effort, including telescopes and airplane instruments. More than half its workers were women. After the war, production switched to manufacturing watchcases, and production rose to 30,000 watchcases per week, mostly for ladies’ watches.
Source: http://nawcc.org/images/stories/2010/articles/2012/396/396_177_184.pdf
It stands to reason that Bulova could have been buying BWCCo product as the company was located "just up the road" and they seem to have been liquidating at that point.