I have an HP Windows 7 laptop.

Check your Power Options as it sounds like it is set to shutdown/sleep after a certain time.

Do a search for Power Options from the start button and change your plan settings.
The first set of options you have include, at the bottom, a Sleep after x minutes option.

If it is literally starting up from a shut down state, then you may have a bad power button or a bad motherboard.

If it is under warranty, take it in.