No theory lives forever, but some live for a helluva long time. Trust me, for example, the results of the Halting Problem will be relevant for a very, very long time.
I suppose I should have made a distinction between research and system development. You are absolutely correct that there are theoretical problems that
are of ongoing interest to CS researchers. You can go back even farther than Turing to find interesting theories.
But until these theories result in practical applications, which is almost always dependent on some advance in hardware, they are only of interest to researchers and academics.
The majority of CS people work in some system development capacity, not in research.