Background/ Objectives: Persistent infections are characterized by recurrent treatment failure and relapse despite apparent antibiotic susceptibility by standard testing, a clinical reality not fully explained by conventional resistance paradigms. Bacterial persister cells, genetically susceptible but phenotypically tolerant subpopulations, survive otherwise lethal antibiotic exposure through reversible physiological adaptations. This review proposes a pharmacological framework linking antimicrobial exposure, bacterial tolerance, persistence, relapse, and the emergence of stable antimicrobial resistance (AMR). Methods: A structured narrative review was conducted using PubMed/MEDLINE, ClinicalTrials.gov, Centers for Disease Control and Prevention (CDC), and World Health Organization/Global Antimicrobial Resistance and Use Surveillance System (WHO/GLASS) sources (inception to 19 June 2026, priority 2010–2026), following Scale for the Assessment of Narrative Review Articles (SANRA) framework principles. Results: Resistance, tolerance, and persistence are pharmacologically distinct phenotypes. Persistence occurs without minimum inhibitory concentration (MIC) elevation and is shaped by antimicrobial exposure, target-site penetration, biofilm barriers, intracellular localization, and host stress. The review operationalizes persistence prevention exposure (PPE) in relation to minimum duration for killing 99%/99.99% of cells (MDK99/MDK99.99), persister fraction, minimum biofilm eradication concentration (MBEC), and biphasic time-kill modeling. Conclusions: Antimicrobial therapy should evolve from a model centered solely on MIC suppression and killing of actively growing bacteria toward one that also includes the prevention and eradication of persister reservoirs. Persistence prevention may reduce relapse, repeated antibiotic exposure, and the evolutionary path toward stable AMR.