Well, I fixed my TM problem last week, and now have a very good understanding of the problem so I thought I would share the solution.
First of all, there are many "solutions" given in this thread. Each one may work for the individual that posted the solution, but in general there is a trend. And this trend indicates that TM has been reset by Apple to have a very low priority. It is possible to up this priority. More on this later but it is not necessary.
However, recognizing that TM has a low priority, if any other application is busy, it will take over the activity, putting to sleep TM. Most of these apps are system related apps. In my case secd was the app that took over.
Activity monitor is the key to diagnosing the problem. Look at the CPU usage, and look at where backupd is listed. Typically, it will by way down the list. Your assignment it to get it first on the list by shutting down anything else that is hogging the CPU, typically system junk. Just don't kill the system stuff, find out by googling the app what it is doing and shut that down. Until you get backupd at the top of the activity CPU usage list, TM sleeps.
I have seen on this thread to turn off wireless, to trash Norton antivirus software and other antivirus products, to turn off many other apps. Obviously, Norton is always running, so it will always shut down backupd, etc.
It is also possible to increase the priority of TM using "nice" and "renice"which is a unix app invoked in terminal. Its not necessary to fix TM this way, but can be done.