Changes in Employment are driven by two processes – Exits and Hires. In fact, we can construct a "Job Accounting Identity":
Change in Employment = Hires – Exits
If 10 people are hired but 20 people exit, the change in employment is -10 (10 – 20 = -10). If 20 people enter the labor force but only 10 leave, then the change in employment is +10 (20 – 10 = 10). More people entering the workforce than leaving is what generates gains in employment.
There are different types of Job Exits. On one hand, there is "natural turnover" in the labor market: maternity leaves, retirements, or promotions are all normal events which can produce a job vacancy. Layoffs, on the other hand, are driven by the economic cycle. Both the normal course of business and cyclical factors drive people to "exit" their jobs.
Abstracting away from cyclical factors (i.e. layoffs), the following example will help clarify how Hiring Demand can grow even as Nonfarm Employment falls. We set the level of initial employment at 1,000 workers and the monthly "turnover rate" at 4% (which is pretty close to the actual monthly turnover rate of the US labor force). The number of Hires grows by 10% every month, but starting from a level that produces employment losses. Even at a constant 4% turnover rate and a 10% growth in Hiring, it still takes the economy 6 months to generate gains in employment.
In other words, Hiring Demand can continue to grow, but as long as it remains below the replacement level Total Nonfarm Employment will continue to shrink.