That is an odd message to receive if you downloaded RStudio recently, since that’s not a recent version. Did you download from here? https://www.rstudio.com/products/rstudio/download/
The file you download should be called RStudio-1.1.456.dmg.
Given your symptoms, I wonder if maybe you didn't actually install RStudio originally? On Mac, RStudio doesn't use an installer wizard. Instead, the app is distributed inside a "disk image" and must be copied to your computer via drag-and-drop.
When you open the .dmg file you downloaded, the disk image will mount. Think of it as being like if you connected a read-only thumb drive containing the app to your computer. You could run the app from that thumb drive, but the app wouldn’t have been copied to your computer. The next time you restarted, the thumb drive would be automatically disconnected and the app would be gone. The same thing happens with disk images.
Here are step by step instructions for how to install an app distributed this way:
http://www.ofzenandcomputing.com/how-to-install-dmg-files-mac/
The appearance of folder and disk icons has changed somewhat since that post was written, but the basic principles still apply. You need to drag the RStudio app from the Disk Image window into your Applications folder in order to actually install it on your computer. Once you’ve done that, you can eject the Disk Image (just like if it was a thumb drive!) and delete the .dmg file.
To run RStudio for the first time after installing, you will need to launch it from your Applications folder. To add it to your Dock, follow these instructions: https://www.imore.com/how-use-dock-your-mac#apps