Mathematical modeling of 176 weeks of GLP-1 receptor agonist treatment reveals weight loss peaks at 24% by week 96, then plateaus for 78 weeks despite continued medication. Energy intake initially drops 32% within four weeks but gradually rises to match energy expenditure by week 98, creating metabolic equilibrium that halts further weight loss. Energy expenditure declines 9.2% and stabilizes, while discontinuation triggers energy intake above baseline levels, causing 5.3% weight regain. This modeling study provides the first quantitative framework for understanding why millions of patients on semaglutide, tirzepatide, and similar medications experience frustrating plateaus despite perfect adherence. The findings challenge the assumption that these drugs provide indefinite weight loss and highlight a critical gap in obesity treatment protocols. The plateau phenomenon suggests that metabolic adaptation overwhelms pharmacological intervention over time, requiring combination strategies. The research supports integrating structured nutrition therapy and behavioral interventions during GLP-1 treatment rather than relying solely on medication. However, this remains theoretical modeling based on a single phenotype rather than diverse real-world populations, limiting immediate clinical application.