The stability of the antioxidant fraction in edible vegetable oils has been evaluated during a simulated deep frying process at 180 °C. Four edible oils (i.e., extra-virgin olive oil with a 400 μg/mL overall content in naturally existing phenols; high-oleic sunflower oil without natural content of these compounds but enriched either with hydrophilic antioxidants isolated from olive pomace or with an oxidation inhibitor, dimethylsiloxane; and sunflower oil without enrichment) were subjected to deep heating consisting of 20 cycles at 180 °C for 5 min each. An oil aliquot was sampled after each heating cycle to study the influence of heating on the antioxidant fraction composed of hydrophilic and lipophilic antioxidants such as phenols and tocopherols, respectively. The decomposition curves for each group of compounds caused by the influence of deep heating were studied to compare their resistance to oxidation. Thus, the suitability of olive pomace as raw material to obtain these compounds offers an excellent alternative to the use of olive-tree materials different from leaves. The enrichment of refined edible oils with natural antioxidants from olive pomace is a sustainable strategy to take benefits from this residue.