Fuzzing nowadays has been commonly modeled as an optimization problem, e.g., maximizing code coverage under a given time budget via typical search-based solutions such as evolutionary algorithms. However, such solutions are widely argued to cause inefficient computing resource usage, i.e., inefficient mutations. To address such issue, two neural program-smoothing-based fuzzers, Neuzz and MTFuzz, have been recently proposed by approximating program branching behaviors via a neural network model which inputs byte sequences of a seed and outputs vectors representing program branching behaviors. Moreover, assuming that mutating the bytes with larger gradients can better explore branching behaviors, they develop strategies to mutate such bytes for generating new seeds as test cases. Although they have been shown to be effective in their original papers, they were only evaluated upon a limited dataset. In addition, it is still unclear how their key technical components and whether other factors can impact their performance. To further investigate neural program-smoothing-based fuzzing, we first construct a large-scale benchmark with a total of 28 influential open-source projects. Then, we extensively evaluate Neuzz and MTFuzz on such benchmark where the results suggest that they can incur quite inconsistent edge coverage performance. Moreover, neither neural network models or mutation strategies can be consistently effective, and the power of their gradient guidance mechanisms have been compromised so far. Inspired by such findings, we propose an improved technique, namely RESuzz, upon neural program-smoothing-based fuzzers by enhancing their adopted gradient guidance mechanisms along with appending the AFL havoc mechanism. Our evaluation results indicate that it can significantly increase the edge coverage performance of Neuzz and MTFuzz. Furthermore, we also reveal multiple practical guidelines to advance future research.