Existing benchmarks for deep research agents (DRAs) assess only single-shot outputs, ignoring a key question: can DRAs improve their reports when guided by feedback? To investigate this, we conduct a multi-turn evaluation of DRAs under two feedback settings: self-reflection, in which the agent revises its report without any external diagnostic signal, and process-level feedback, in which the agent receives guidance targeting gaps in its research strategy. To enable process-level feedback, we design Research Gap Inference (RGI), a method that analyzes patterns of satisfied and unsatisfied rubric criteria to infer research-process gaps. Our analysis reveals three key findings: (i) under self-reflection, agents incorporate and regress on rubric criteria at nearly equal rates, yielding negligible net improvement; (ii) a single round of process-level feedback yields substantial gains, raising the normalized score by approximately $8$-$15$ points and yielding a roughly $35$-$40\%$ incorporation rate; (iii) these gains do not compound over subsequent turns, as agents regress on up to $24\%$ of previously satisfied criteria when rewriting the full report to address remaining gaps. Even with targeted guidance, reliable multi-turn improvement remains out of reach for the DRA architectures we evaluate. Our code and results are publicly available at https://github.com/sabharwalrishabh/Multi-Turn-Evaluation-of-DRAs.