No, a natural tan from sun exposure is not permanent. While a tan might last for several weeks, it will eventually fade. This is because your skin naturally sheds its cells, and the tanned skin cells are replaced with new, untanned ones. This process causes the tan to disappear gradually. Many sources confirm this. For example, Healthline states that "A tan is never permanent because skin naturally exfoliates itself over time. This causes the tanned skin to flake off. New cells are formed and..." Similarly, Hawaiian Tropic notes that "Unfortunately, a natural tan doesn't last forever and will eventually fade away."
However, there are companies offering spray tans or other treatments that claim to provide a "permanent tan". These treatments may provide a longer-lasting color than a natural tan, but they are not truly permanent. The longevity will vary based on the specific treatment and individual skin type. A website such as RealTanContact advertises a "Sun-Kissed Glow That Lasts Years," but this should be viewed with skepticism and requires further verification of their claims. The term "permanent" in this context is likely used for marketing purposes. It's crucial to distinguish between a long-lasting cosmetic tan and a true, genetically determined skin pigmentation.
One Reddit post (https://www.reddit.com/r/CasualConversation/comments/qha3z1/unpopular_fact_tans_can_be_permanent/) mentions an anecdote about a person with a long-lasting tan, but this is an exception rather than the rule, and likely isn't representative of a true "permanent tan" resulting from sun exposure.