How is your system working exactly? I always use a combination of software and hardware watchdogs. Let me explain...
My example assumes you're working with a preemptive real time kernel and you have watchdog support in your cpu/microcontroller. This watchdog will perform a reset if it was not kicked withing a certain period of time. You want to check two things:
1) The periodic system timer ("RTOS clock") is running (if not, functions like "sleep" would no longer work and your system is unusable).
2) All threads can run withing a reasonable period of time.
My RTOS (www.lieron.be/micror2k) provides the possibility to run code in the RTOS clock interrupt handler. This is the only place where you refresh the hardware watchdog, so you're sure the clock is running all the time (if not the watchdog will reset your system).
In the idle thread (always running at lowest priority), a "software watchdog" is refreshed. This is simply setting a variable to a certain value (e.g. 1000). In the RTOS clock interrupt (where you kick the hardware watchdog), you decrement and check this value. If it reaches 0, it means that the idle thread has not run for 1000 clock ticks and you reboot the system (can be done by looping indefinitely inside the interrupt handler to let the hardware watchdog reboot).
Now for your original question. I assume the system clock keeps running, so it's the software watchdog that resets the system. In the RTOS clock interrupt handler, you can do some "statistics gathering" in case the software watchdog situation occurs. Instead of resetting the system, you can see what thread is running at each clock tick (after the problem occurs) and try to find out what's going on. It's not ideal, but it will help.
Another option is to add several software watchdogs at different priorities. Have the idle thread set VariableA to 1000 and have a (dedicated) medium priority thread set Variable B. In the RTOS clock interrupt handler, you check both variables. With this information you know if the looping thread has a priority higher then "medium" or lower then "medium". If you wish you can add a 3rd or 4th or how many software watchdogs you like. Worst case, add a software watchdog for each priority that's used (will cost you as many extra threads though).