Trying to think what would cause mouse click to work after a period of time.
First thing I thought of was some software (like a click-macro utility) grabbing control of the mouse click, then letting go when done or timed out. Makes no sense.
Other thing I could think of was USB port power issue, which also doesn't make a lot of sense. If there is any other USB device attached, disable it. If you have an externally powered USB hub available to you, you could try that.