I am using LPCXpresso V8.2.0 for LPC812. My project was working fine. I wanted to write a document on how to setup the software for a new employee, so I deleted the project by right-clicking and "Delete". After I clicked on File-Import. Under "General", I chose "Existing Projects into Workspace" and selected the folder where my project is. When I go to my build configurations, I only see "Default". Before, I had "Debug" and "Release". Also, I cannot compile anymore, I have the error "Error: Program "make" not found in PATH".
So you deleted a project, then expected to still be able to use it? Not something we would generally recommend - certainly without making a backup first (for example by using the Quickstart -> Export to zip option) !
I'm also not sure that I follow why you think this is a good thing to describe to a new employee.
That aside, I have just tried the process that you describe, and my project imported back into the workspace appears to function correctly. The only thing that I can think of is that you managed to delete or modify 1 or more of the files from within the project itself somehow (in particular the .cproject and/or .project), rather than just deleting the metadata that describes the project's existence in the workspace
I am sorry to say that you be better off creating a new project, then copying the files from your original project into it.