How does a planet become depleted and how to recover it

From what I've seen during play, your best system will trade with their best system. From there it works its way down until you run out of available systems, or they do.

When you add a new possible trade route or improve the trade bonus on a system, the game re-calculates the trade network. This means your systems can "steal" trade from a "lesser" system in your empire in the trade network.

If you colonize a system outside of your colored influence area you create an outpost which carries this penalty. After 30 turns without being blockaded, your outpost becomes a colony and therefore generates its own influence area thus removing the penalty and starts to get the expansion disapproval as Garm stated in the question comments.

As far as I know, if another Planets influence area covers your outpost it wont get this penalty and will instead instantly get the expansion disapproval.