Apple isn't reviving the 4-inch iPhone
In a note to investors (thanks, MacRumors) he said,
As there is still demand for a 4-inch iPhone, we believe Apple will upgrade this product line. Because the iPhone 5s is more popular than the iPhone 5c, we think Apple is likely to launch an upgraded iPhone 5s. We predict Apple will mass-produce this new 4-inch iPhone in [the first half of 2016] with metal casings. In order to make the current iOS 9 or next-generation iOS 10 run smoothly, Apple may adopt an A9 chip for this new phone.
Apple still sells the iPhone 5s as its entry price point smartphone, and part of what keeps that price low is the fact that manufacturing costs are lower since the model is a couple years old. It runs iOS 9, just like the iPhone 6s, but is missing some features that require the newer hardware.
Assuming Apple does update the iPhone 5s with new internal components, including the A9 processor, the price will go up. If Apple is looking to keep an low cost entry point in the iPhone line up, increasing the cost for its 4-inch display model doesn't fit with its game plan. Price isn't, however, typically a driving point in Apple's iPhone strategy.
This isn't the first time predictions of a new small screen iPhone have cropped up, which isn't surprising considering some users aren't interested in the larger 4.7-inch and 5.5-inch screens on the iPhone 6 and iPhone 6s lines. So far, those predictions haven't panned out, and I doubt they will this time, too.
Apple has moved on from the smaller screen form factor, and the iPhone 5s is still around because it's cheap to make and serves as an easy entry point into the company's ecosystem. Once the value in the iPhone 5s is gone for Apple, it'll be retired, just like so many other iPhone models before it.
Apple routinely leaves its older technology and designs behind, along with the customers that aren't interested in moving on to newer products. It'll be the same for the iPhone 5s and the 4-inch display.