Seawater, in essence, lasts indefinitely due to the Earth's atmosphere and natural water cycle.
Our planet operates within a closed system regarding water. The water on Earth today is essentially the same water that has been here for millions of years. The atmosphere traps the water, facilitating a continuous cycle of evaporation, condensation, and precipitation.
Even if we were to begin desalinating large quantities of seawater for human consumption and other uses, the overall quantity of water on Earth would remain constant. While ocean levels might decrease slightly as water is extracted and distributed inland, the water would eventually return to the oceans through various means, such as rivers, runoff, and treated wastewater.
Therefore, seawater doesn't "expire" or disappear. It's constantly being recycled and renewed within the Earth's water cycle.