Persistent Web information assistants must combine evolving document facts with user requirements established and revised across sessions. Yet systematic evaluation of how changes in both sources affect response requirements and evidence attribution remains limited. To address this gap, we introduce Dual-Source Evolution Benchmark (DuSE-Bench), a benchmark comprising 1,000 tasks across five scenarios, including 700 whose required premises originate in both dialogue and documents. An evolving Support Graph guides task construction and preserves links from updated facts and reused conclusions to original turns and passages. Task annotations distinguish grounding source from state dependence and enable separate evaluation of response content, response type, and source attribution. Experiments across 11 baseline configurations reveal persistent challenges in joint reasoning over evolving dialogue and documents, with content accuracy on jointly grounded tasks reaching at most 56.7%. Moreover, improvements in content accuracy can coincide with poorer response choice, while content-correct responses frequently lack complete attribution to original evidence. Matched evidence substitutions further show that the effect of replacing one source's evidence depends on support from the other. These findings motivate coordinating dialogue memory and document retrieval to apply current user requirements and document facts together while preserving their original support. The data are available at https://github.com/JianfengGao7/DuSE-Bench.

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