Renamon is based on / heavily influenced by the Japanese kitsune, which have mystical abilities, most famously that of illusions. On top of that, Renamon has ninja-like speed, and I'd say it's a combination of both that it's using here.
Blink an eye and you'll miss it. One moment it's there, the next it's gone and only leaves a fading stand-in illusion of itself (what a trickster), as it's probably hiding away in the shadows or trees. Or it's actually using illusion abilities to straight up become invisible for extended periods of time (that would have to be harder to keep up, but who knows).
Point being, these abilities would have to be balanced for fights - can't just have Renamon "godmode" and stay completely invisible, after all. That's why I'm assuming it has to stand completely still and concentrate to actually become and stay invisible, and therefore, using it's speed to jump away and leaving behind a stand-in illusion from it's physical hiding place would be less taxing and preferable, whenever possible.
A kitsune's mystical powers increase with age and amount of tails they have - from one, up to nine tails (see Kyubimon, Renamon's Champion level). Ninetales from Pokémon, nine-tails Kurama (Kyuubi) from Naruto... kitsune are a big, big thing in Japanese mythology.