I'm not sure what you mean by "Continuous use counter" but I can explain how Weblogic threads work and hopefully that will clarify your doubt.
Each incoming request is assigned one thread by WL. This thread will be utilized to complete the request and then returned to the thread pool.
What StuckThreadMaxTime does is to report that the thread has crossed that time limit for the same request.
So if it is set at default of 600 seconds, a message will be logged when that time is crossed.
Note - Weblogic does NOT clear that stuck thread after 600 seconds, it will continue the processing for as long as it needs. It merely notes this event in the log.
Finally when the request is completed, the thread is available for the next request. You can verify how many requests each thread has completed by viewing in the Admin console
Servers > Monitoring > Threads will show the number of threads and how many completed requests
So to come back to your exact question - the StuckThreadMaxTime is reset for each request and not carried across over multiple requests
This timer starts at the time of the request, and not when the thread was returned to the pool.
You can verify this via thread dumps - if you get a StuckThread message for (say) Thread 7 but after few minutes you can see Thread 7 might have cleared and is now serving another request.
Further Reading:
WebLogic stuck thread protection