Early detection of cognitive decline is crucial for enabling interventions that can slow neurodegenerative disease progression. Traditional diagnostic approaches rely on labor-intensive clinical assessments, which are impractical for frequent monitoring. Our pilot study investigates voice assistant systems (VAS) as non-invasive tools for detecting cognitive decline through longitudinal analysis of speech patterns in voice commands. Over an 18-month period, we collected voice commands from 35 older adults, with 15 participants providing daily at-home VAS interactions. To address the challenges of analyzing these short, unstructured and noisy commands, we propose Cog-TiPRO, a framework that combines (1) LLM-driven iterative prompt refinement for linguistic feature extraction, (2) HuBERT-based acoustic feature extraction, and (3) transformer-based temporal modeling. Using iTransformer, our approach achieves 73.80% accuracy and 72.67% F1-score in detecting MCI, outperforming its baseline by 27.13%. Through our LLM approach, we identify linguistic features that uniquely characterize everyday command usage patterns in individuals experiencing cognitive decline.