Software engineering (SE) agents powered by large language models are increasingly adopted in practice, yet they often incur substantial monetary cost. We introduce EET, an experience-driven early termination approach that reduces the cost of SE agents while preserving task performance. EET extracts structured experience from prior issue-resolution executions and leverages it to guide early termination during patch generation and selection, reducing unproductive iterations. We evaluate EET on the SWE-bench Verified benchmark across three representative SE agents. EET consistently reduces total cost by 19%-55% (32% on average), with negligible loss in resolution rate (at most 0.2%). These efficiency gains are achieved, on average, by identifying early-termination opportunities for 11% of issues and reducing API calls, input tokens, and output tokens by 21%, 30%, and 25%, respectively. We release the code, prompts, and data at https://github.com/IanWalls/EET.