Efficient resource orchestration in modern edge computing deployments is increasingly challenged by node mobility, stochastic workloads, and limited energy budgets. Conventional static and heuristic scheduling methods are fundamentally inadequate for volatile environments such as UAV swarms and vehicular ad hoc networks, where topology and resource availability evolve continuously. This paper proposes a novel adaptive resource management framework grounded in Proximal Policy Optimization (PPO), a state-of-the-art Deep Reinforcement Learning (DRL) algorithm, tailored for ephemeral edge computing scenarios. The resource allocation problem is rigorously formalized as a Markov Decision Process (MDP) that jointly accounts for end-to-end task latency, cumulative energy expenditure, load distribution fairness, and Service Level Agreement (SLA) compliance. Through iterative interaction with a realistic simulation environment encompassing 20 mobile UAV nodes, the PPO agent acquires nuanced allocation policies that balance competing performance objectives. Our key novelty lies in a composite reward signal that explicitly penalizes battery depletion events, discouraging greedy local processing in favor of energy-balanced, network-lifetime-aware decisions. Experimental results demonstrate that the proposed PPO-based framework reduces SLA violations by approximately 30% and extends network operational lifetime by up to 47% compared to Deep Q-Network (DQN) baselines and classical static schedulers.