If it is a "No Timeout" license, the Desktop license will stay active until it has been authorized. If have an active license which you are unable to authorize, get in touch with the Esri Technical Support team.
If it is a Educational site license, you need to contact the GIS coordinator of your institute, who manages the licensing, to know about the expiration date.
If you are asking about the trial license, it will stay active for 60 days from the date you created the trial account.
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