There is not a set time period when you should replace your pick. Instead, most experienced guitarists recommend that you do so whenever the tip of the pick gets worn out. Depending on how often you play the guitar, you might have to change the pick once every couple of hours when you are performing or once every few months.
If you have a favorite pick that you do not want to replace, you can use some sandpaper to sharpen its tip. However, doing so repeatedly might cause the model to lose its shape. Given that most pick sets include 12 or more units, you will surely always have a pick that you can utilize instead of the one that you already use.
On top of that, generally speaking, if you rarely play the guitar, chances are that you won’t need to replace the pick too often.