I have a frew breakpoints set in my main file (index.php) along with the files that are referenced with require(). These breakpoints are all reached by the debugger. However, once the final require() file is processed, I see that the debug session is finished in the log window. After this, the breakpoints I have set in other files, which should be triggered by navigation through the Output window, are not hit.

How do I prevent the debug session from terminating?

breakpoints are set by IDE and work during debug session only. They should not be hit by any other way including navigation.

Although, you can't prevent debug session from terminating. It finishes when PHP finishes the request.
Each subsequent request leads to completely new session and if it is not a debug session you won't see any breakpoint hits.

Interesting. Can you explain to me how the product can really be useful if you can't step through the operation of a complex site? Isn't clicking through various pages exactly what PHP is all about?

No one cares to elaborate on this issue? Can someone explain to me how debugging a single web page is worth purchasing the product? There must be a way to get this tool to be useful on multiple pages.

Actually it works fine for multiple pages.
Common scenario is per following:
You open a page in the debugger
Click continue (F9)
Get it finished and form inputs shown on the output tab
You fill inputs and click submit button
PHPED opens the target script in the debugger and you can decide whether you want to bypass till the next page or step though it.