Is this a common problem? In a word Yes every d800 has this issue!
Yes, and you can safely expand this to: Every digital camera has this issue.
There are two major noise contributions - read out noise and thermal noise. As the exposures time increases so does the thermal noise, but the read out noise stays the same.
The read out noise dominate in the short exposures and the thermal noise dominate in the long exposures (rough generalisation). The thermal noise will also increase with the ambient temperature.
I have had communication with Nikon about this and nothing can be done apart from using in camera LENR which of course doubles your exposure time and is hardly useable for multiple long exposures.
You can shoot a dark frame often done by astronomical photographers and then subtract from this in photoshop but you will need to read up on the technique.
In camera LENR automates dark frame subtraction by taking a single dark frame of equal exposure time and subtracting it from the picture. If you don't want to loose the extra time used for automatic dark frame exposure and subtraction, you can just do this manually after the shoot.
Take your pictures with a fixed exposure time without LENR. When you're done and while you're packing up the equipment, let the camera take some dark frames with the lense cap on and the same exposure time.
When you get back you can subtract the dark frame from all the pictures. If you want to increase the quality of the dark frame you can take a number of dark frames (perhabs 16 or something similar) and average these before subtraction. This will reduce random noise from the dark frames.