Within the past 3 days, I ran outof neurotin fir diabetic neuropathy. I am experiencing bad depression. Is this a function of stopping neurotin?

Neurontin (gabapentin) It is very likely due to stopping Neurontin (gabapentin) precipitously. Neurontin (gabapentin) needs to be tapered over >7days when discontinuing because of the risk of withdrawal.
YES. Neurontin (gabapentin) is a seizure medication that is effective in neuropathic pain. Off label it has mood stabilizing properties also. So you could be experiencing both increased pain and a sudden stop of a med that my have been helping with your mood. So i don't believe stopping it caused a clinical depression, but could certainly lower your mood and energy levels. Sounds like a refil is in order.
It may be. Please notify your doctor immediately to that you can restart your neurotin.