Defrag is being triggered 3 or 4 times a day.There is no Task Scheduler entry that would correspond.The log always shows"defrag ended successfully" but"defrag started" seems to be missing.I can't see any clues as to what is causing this.

Actually, if you go back to the Task Scheduler and navigate down to Task Scheduler Library >> Microsoft >> Windows >> Defrag. Your default entry probably has it to run every day at 1:00 AM. However, if you look at the Conditions tab, you will see that the task is set to stop when the computer is no longer idle and restart when the idle state resumes. This could explain why it seems that defrag runs three to four times a day.

I don't think so. The defrag logs: "The disk defragmenter successfully completed defragmentation on (C:)"This doesn't look like a "defragmenter paused because computer was no longer idle" event.