The rise of context-aware IoT applications has increased the demand for timely and accurate context information. Context is derived by aggregating and inferring from dynamic IoT data, making it highly volatile and posing challenges in maintaining freshness and real-time accessibility. Caching is a potential solution, but traditional policies struggle with the transient nature of context in IoT (e.g., ensuring real-time access for frequent queries or handling fast-changing data). To address this, we propose the Dynamic Context Monitoring Framework (DCMF) to enhance context caching in Context Management Platforms (CMPs) by dynamically evaluating and managing context. DCMF comprises two core components: the Context Evaluation Engine (CEE) and the Context Management Module (CMM). The CEE calculates the Probability of Access (PoA) using parameters such as Quality of Service (QoS), Quality of Context (QoC), Cost of Context (CoC), timeliness, and Service Level Agreements (SLAs), assigning weights to assess access likelihood. Based on this, the CMM applies a hybrid Dempster-Shafer approach to manage Context Freshness (CF), updating belief levels and confidence scores to determine whether to cache, evict, or refresh context items. We implemented DCMF in a Context-as-a-Service (CoaaS) platform and evaluated it using real-world smart city data, particularly traffic and roadwork scenarios. Results show DCMF achieves a 12.5% higher cache hit rate and reduces cache expiry by up to 60% compared to the m-CAC technique, ensuring timely delivery of relevant context and reduced latency. These results demonstrate DCMF's scalability and suitability for dynamic context-aware IoT environments.