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Deploying services efficiently while satisfying their quality requirements is a major challenge in network slicing. Effective solutions place instances of the services' virtual network functions (VNFs) at different locations of the cellular infrastructure and manage such instances by scaling them as needed. In this work, we address the above problem and the very relevant aspect of sub-slice reuse among different services. Further, unlike prior art, we account for the services' finite lifetime and time-varying traffic load. We identify two major sources of inefficiency in service management: (i) the overspending of computing resources due to traffic of multiple services with different latency requirements being processed by the same virtual machine (VM), and (ii) the poor packing of traffic processing requests in the same VM, leading to opening more VMs than necessary. To cope with the above issues, we devise an algorithm, called REShare, that can dynamically adapt to the system's operational conditions and find an optimal trade-off between the aforementioned opposite requirements. We prove that REShare has low algorithmic complexity and is asymptotic 2-competitive under a non-decreasing load. Numerical results, leveraging real-world scenarios, show that our solution outperforms alternatives, swiftly adapting to time-varying conditions and reducing service cost by over 25%.