Automated issue solving seeks to autonomously identify and repair defective code snippets across an entire codebase. SWE-Bench has emerged as the most widely adopted benchmark for evaluating progress in this area. While LLM-based agentic tools show great promise, they still fail on a substantial portion of tasks. Moreover, current evaluations primarily report aggregate issue-solving rates, which obscure the underlying causes of success and failure, making it challenging to diagnose model weaknesses or guide targeted improvements. To bridge this gap, we first analyze the performance and efficiency of three SOTA tools, spanning both pipeline-based and agentic architectures, in automated issue solving tasks of SWE-Bench-Verified under varying task characteristics. Furthermore, to move from high-level performance metrics to underlying cause analysis, we conducted a systematic manual analysis of 150 failed instances. From this analysis, we developed a comprehensive taxonomy of failure modes comprising 3 primary phases, 9 main categories, and 25 fine-grained subcategories. Then we systematically analyze the distribution of the identified failure modes, the results reveal distinct failure fingerprints between the two architectural paradigms, with the majority of agentic failures stemming from flawed reasoning and cognitive deadlocks. Motivated by these insights, we propose a collaborative Expert-Executor framework. It introduces a supervisory Expert agent tasked with providing strategic oversight and course-correction for a primary Executor agent. This architecture is designed to correct flawed reasoning and break the cognitive deadlocks that frequently lead to failure. Experiments show that our framework solves 22.2% of previously intractable issues for a leading single agent. These findings pave the way for building more robust agents through diagnostic evaluation and collaborative design.