I am not a professional photographer but shoot outdoor and indoor pictures, weddings, and portraits as a hobby. I use a Nikon D750 with a 70-200mm 2.8 VR lens and a 35mm 1.8 ED lens. I have been having focus problems with both lens while shooting in low light. The camera tries to focus but is unable to do so. It occurs more often with the 70-200mm lens and while I am using the camera's flash. What could be causing this problem?
The problem is lack of enough light to create enough contrast between the darkest and brightest parts of the scene within the area(s) covered by your active focus point(s).
The reason you are experiencing the problem more with the 70-200mm f/2.8 lens than the 35mm f/1.8 lens is that the 35mm lens is a tad over one stop faster and will let in just over twice as much light as the 70-200mm lens. Remember that metering and AF are done with the lens wide open regardless of your aperture setting. The lens is only stopped down the instant before the shutter opens.
One thing that might help is to select only AF points that are more sensitive at wider apertures, are "cross type" AF points, or are both. I'm not very familiar with the AF system of the D750 and Nikon is notorious for keeping info about the AF points in their cameras close to the vest, but you might find the information somewhere if you look for it. It would be easy enough for a third party to deduce using comprehensive testing.
Note that the -3EV maximum sensitivity of the D750's AF system is almost certainly measured using only the center focus point. It's just the laws of physics. The center focus point will always enjoy the advantage of more light than any of the other focus points. The further away from center a focus point is, the less sensitive it can be due to the way the light from each side of the lens is split. So when in very low light and your camera is having trouble finding focus try using only the center point and see if that helps.