Logic optimization constitutes a critical phase within the Electronic Design Automation (EDA) flow, essential for achieving desired circuit power, performance, and area (PPA) targets. These logic circuits are typically represented as Directed Acyclic Graphs (DAGs), where the structural depth, quantified by node level, critically correlates with timing performance. Modern optimization strategies frequently employ iterative, local transformation heuristics (\emph{e.g.,} \emph{rewrite}, \emph{refactor}) directly on this DAG structure. As optimization continuously modifies the graph locally, node levels require frequent dynamic updates to guide subsequent decisions. However, a significant gap exists: existing algorithms for incrementally updating node levels are unbounded to small changes. This leads to a total of worst complexity in $O(|V|^2)$ for given local subgraphs $\{ΔG_i\}_{i=1}^{|V|}$ updates on DAG $G(V,E)$. This unbounded nature poses a severe efficiency bottleneck, hindering the scalability of optimization flows, particularly when applied to large circuit designs prevalent today. In this paper, we analyze the dynamic level maintenance problem endemic to iterative logic optimization, framing it through the lens of partial topological order. Building upon the analysis, we present the first bounded algorithm for maintaining level constraints, with $O(|V| Δ\log Δ)$ time for a sequence $|V|$ of updates $\{ΔG_i\}$, where $Δ= \max_i \|ΔG_i\|$ denotes the maximum extended size of $ΔG_i$. Experiments on comprehensive benchmarks show our algorithm enables an average 6.4$\times$ overall speedup relative to \rw and \rf, driven by a 1074.8$\times$ speedup in the level maintenance, all without any quality sacrifice.