The following documented studies demonstrate the value and pay back of advertise in a recessionary period?
In a study of U.S. recessions, McGraw-Hill Research analyzed 600 companies from 1980-1985. The results showed that business-to-business Firms that Maintained or Increased their Advertising Expenditures during the 1981-1982 recession Averaged Significantly Higher Sales growth, both during the recession and for the following three years, than those that eliminated or decreased advertising. By 1985, sales of companies that were Aggressive Recession Advertisers had Risen 256% over those that didn't keep up their advertising.
In analysis of the 1990-91 recession, Penton Research Services, Coopers & Lybrand, in conjunction with Business Science International, found that better performing businesses focused on a strong marketing program enabling them to solidify their customer base, take business away from less aggressive competitors, and position themselves for future growth during the recovery.
A series of six studies conducted by the research firm of Meldrum & Fewsmith showed conclusively that Advertising Aggressively during Recessions not only Increases Sales but Increases Profits. This fact has held true for all post-World War II recessions studied by The American Business Press starting in 1949.

A report by Frankenberger and Graham extend the investigation of recessionary advertising spending increases and decreases to include financial measures of performance, and compare performance across consumer products, industrial products, and services industries. They conduct an econometric analysis employing cross-sectional time series regression on a sample of 2,662 firms over 16,147 firm-years.

They analyze the economy-wide and industry-specific effects that average advertising spending has on earnings and market value, and compare those effects with the effects of increased and decreased advertising spending during recessionary periods.

Their results indicate that advertising creates a firm asset by contributing to financial performance for up to three years in the future. Further, increasing spending on advertising during a recession leads to benefits that exceed the benefits of increasing advertising during non recessionary times. However, the effect varies by industry: A performance boost is observed during the recession year and one year following for consumer and industrial products firms, but not for services firms. When firms decrease their advertising during recession, financial performance is eroded only for industrial products firms, and only during the year of the recession.

Frankenberger and Graham conclude that firms should support advertising budgets whenever possible, as advertising in general translates to an asset that is valued by stock market participants. For firms experiencing soft economies in the consumer and industrial products industries, it makes sense to increase budgets during a recession to realize an incremental gain in financial performance. Firms that decide to cut advertising spending during a recession may do so with little cost beyond the recessionary year.