Kimchi doesn't go bad as long as you store the Kimchi properly.
Generally Kimchi when stored properly just ripens the older it gets and doesn't spoil.
If the Kimchi isn't stored properly then it could spoil but as long as you keep the Kimchi stored like it should be then the Kimchi can usually last 20 years or longer but over that time it would just get riper and riper.
As Kimchi gets older and ripens it gets a sour taste to it which doesn't mean it's bad but the sour taste may be too sour for some people.
But you can put the sour tasting Kimchi into foods such as stews and stir fries and the sour taste will not be as noticeable.
When not using the Kimchi make sure it stays sealed until you're ready to use it and I would also recommend putting it in the refrigerator once you open it.