Point-based interactive image segmentation can ease the burden of mask annotation in applications such as semantic segmentation and image editing. However, fully extracting the target mask with limited user inputs remains challenging. We introduce a novel method, Variance-Insensitive and Target-Preserving Mask Refinement to enhance segmentation quality with fewer user inputs. Regarding the last segmentation result as the initial mask, an iterative refinement process is commonly employed to continually enhance the initial mask. Nevertheless, conventional techniques suffer from sensitivity to the variance in the initial mask. To circumvent this problem, our proposed method incorporates a mask matching algorithm for ensuring consistent inferences from different types of initial masks. We also introduce a target-aware zooming algorithm to preserve object information during downsampling, balancing efficiency and accuracy. Experiments on GrabCut, Berkeley, SBD, and DAVIS datasets demonstrate our method's state-of-the-art performance in interactive image segmentation.