How do you maintain consistency in character design and style across multiple episodes or issues?

The ideal situation would be to have a full color character sheet, developed along with your client featuring the character, front and back, so you can use it as a reference. That way you can always have a reference every time you start a new page or a new episode. The character sheet should have also a zoomed in depiction of the face of your character. 

Choose some face or hair features that make your character recognizable and that you can use as "anchors" so people can recognize them, even if they are depicted from far away. 

When you work in digital format, you can just copy-paste faces from other pages, and use them as a reference for new pages, or even have a specific layer with your preferred expressions from that specific character so you can always come back and "inhale" the emotion and vibe they give out so you can bring them alive in the same way.

Even when characters face new situations, try to always connect to the general emotions and reactions from your character, as they also help the reader perceive consistency in the character, even if they change clothes or hairstyles.

In general, consistency and continuity are hard to achieve but never impossible if you have certain order and references laying around.