Influence maximization in temporal social networks presents unique challenges due to the dynamic interactions that evolve over time. Traditional diffusion models often fall short in capturing the real-world complexities of active-inactive transitions among nodes, obscuring the true behavior of influence spread. In dynamic networks, nodes do not simply transition to an active state once; rather, they can oscillate between active and inactive states, with the potential for reactivation and reinforcement over time. This reactivation allows previously influenced nodes to regain influence potency, enhancing their ability to spread influence to others and amplifying the overall diffusion process. Ignoring these transitions can thus conceal the cumulative impact of influence, making it essential to account for them in any effective diffusion model. To address these challenges, we introduce the Continuous Persistent Susceptible-Infected Model with Reinforcement and Re-activation (cpSI-R), which explicitly incorporates active-inactive transitions, capturing the progressive reinforcement that makes nodes more potent spreaders upon reactivation. This model naturally leads to a submodular and monotone objective function, which supports efficient optimization for seed selection in influence maximization tasks. Alongside cpSI-R, we propose an efficient temporal snapshot sampling method, simplifying the analysis of evolving networks. We then adapt the prior algorithms of seed selection to our model and sampling strategy, resulting in reduced computational costs and enhanced seed selection efficiency. Experimental evaluations on diverse datasets demonstrate substantial improvements in performance over baseline methods, underscoring the effectiveness of cpSI-R for real-world temporal networks