TD on my puter at work and my iPhone isn't happening. I've marked a task complete a number of times on my iPhone, but it isn't getting marked complete online. If I close my iPhone TD app after I mark the task done, then re-open it, the task isn't marked done anymore - it keeps clearing the checkbox. And yes, the task is a repeating task, but the date due is not changing, so it's not the next recurrence that I'm seeing.
I suspect that the task is set to repeat from "completion date" which means that even if you complete it multiple times, its date will stay the same because the completion date is staying the same. Try changing this to repeat from "due date".
You can also show the completed tasks and youll probably see lots of completed copies of the task.