we have a 9 month old puppy. She is great about using her dog door all day and even at night while we are still up. After we go to bed she will do her business right next to the dog door inside. We leave a light on for her inside and outside but it doesn't seem to help. Any suggestions would be appreciated. Thanks.
It's dark outside and there might be scary things.
We don't know the breed/size of your dog, but considering there's the possibility to use a dog door, I don't expect this to be any bigger dog. As such predators might be a problem the dog fears (and this is perfectly fine and a good thing).
As a solution I'd simply suggest not relying on the dog door to do the "work" for you. Get the dog outside right before you go to bed and you should probably be fine. You probably can't convince/force the dog to go outside alone at night and I wouldn't do so either.
Poor puppy! Also, not so much fun for whoever has to clean it up. A dog that age, though, should be able to go 8 hours without urinating.
Expecting a puppy to go outside alone at night might be asking too much, even if there's a light. It's easier to just have an "accident" in the house.
If a dog can smell any trace of its urine, it will often continue to have "accidents" in the same spot. It's important to decrease the temptation by getting all the smell out of a floor that a dog's urinated on. If it's carpet or wood, an enzyme solution works well. If it's vinyl, it probably isn't necessary, but I still use it on vinyl.
If you don't want to crate her when you go to bed, you could try putting a pad by the door with the doggie door. I used to (very conscientiously) breed border collies*, and puppy accidents were common. One product I was amazed with was Simple Solution puppy training pads. Not only did they protect the floor, but the puppies went straight for them (I also used plain Chux; there was no comparison.)
My guess is that it would be easier if you broke her of the habit entirely. You can do this by crating her after you go out with her the last time (so you know she has urinated.) The crate should be only slightly larger than she can comfortably stand and turn around in. After several weeks of crating her at night without an accident, she should be broken of the habit of urinating during the night.
*I was quite dedicated to breeding to improve the breed, not for financial gain. My dogs were PennHipped at >90%ile and had no genetic abnormalities (Collie Eye Anomaly Clear), and seizure free. They were from herding stock (one from Scotland), and were sold mostly to farmers as working dogs, or people who wanted a dog who excelled at agility. All were ABCA registered. (It's a big deal for Border Collies to be ABCA registered, not AKC.) Looking back on it all, I'm pretty sure I lost a fair amount of money on the whole thing, but I still get calls from people looking for a second dog or from referrals, though I haven't bred in a number of years.