The Shiny Server software stops once the license expires.
RStudio gives you ample notice that the expiration date is coming. Forty-five days in advance, a warning is displayed on the dashboard.
If you intend to keep our product and you miss the expiration date renewal or know you will have problems, RStudio does not want to leave you stranded. Please contact us and let us know what is happening - we'll do what we can to bridge you over until the license renewal purchase is complete.