The counts use distinct CIKs that filed a 10-K or 10-Q form type during the period. 10-K form types include 10-K, 10KSB, 10-K405. 10-Q form types inlude 10-Q and 10QSB. Entities using the asset backed SIC code are excluded. Period dates are adjusted to handle the extended filing deadlines for 10-Ks. Period 1 for the K is February thru April. Period 2 is May thru July etc. Periods for the Qs are calendar year quarters.
The drop in the number of entities filing forms 10-K or 10-Q is roughly 3,500, which is a decline of 28% from the peak, and the decline was more of less continuous for the entire time period, which includes the tech bust, the subsequent period of economic growth, and the financial crisis. It happened despite the fact that a tax break for dividends received from C corporations (which includes all publicly held corporations) was established during this time period and has not been repealed.
The numbers could have declined for a variety of reasons, including consolidation and merger of companies, companies going out of business, and "going private" transactions. Given the continuity of the trend, which coincided with the rise of private equity funds and hedge funds, I suspect that the bulk of the change is due to "going private" transactions. Ruminations on the management advantage of private equity firm organization are found here.