The reason behind why most desk fans get louder over time is the dust and debris build-up. This dust can lead to the fan blades making jittering sounds as it runs, and can inhibit your fan’s overall performance as well.
Also, allowing dust to build upon your fan is not healthy, since it could mix the dust with the air it blows thereby dirtying the air and making it unsafe.
If your fan is having noise issues due to dirt build-up, the best thing, sorry, the only thing to do would be to clean it. Now, some fans are designed to make it easy for you to clean them often, so getting a desk fan that adds that feature is great in terms of cleaning.
Another reason that could cause your fan to make noise is if the blades are somehow touching their protective case.
In this case, you’d hear something like a shrilling or scraping noise whenever the fan runs. Sometimes, the fault is from the product, and sometimes, all you need to do is to adjust the tilt of the fan’s head for the noise to stop.
Other sources of noise in the fan can come from the motor or loose fasteners.