I will admit that my idea of "secure" has changed drastically from when I first built my coop and run. Is your coop surrounded by a hardware cloth apron to prevent digging predators? If there is a way into the run predators will find it. Once inside the run, an open pop door is practically an invitation to chicken dinner. If you have any doubts about the security of your run then continue to close the door at night. Perhaps post a photo of your coop and others can offer their opinions and suggestions as to the level of security it offers.