Once you put something big in the LEO, you'll have to be able to boost its orbit indefinitely, because the orbit will otherwise slowly decay.
https://www.esa.int/Enabling_Support/Space_Engineering_Techn...
But yes, eventually things decay.
https://commons.wikimedia.org/wiki/File:Orbital_Debris_Lifet...
(I may be misremembering or getting confused with a thing specific to tidal locking?)
I suppose the same effect is there with satellites much smaller than the moon, but it would be tiny.