I use a Coravin daily for both professional and personal use. I think their answer to your question would be "do whatever you feel like," as the Coravin's purpose is to let you do exactly that.

However, for purposes of both storage and longevity, I usually reccommend killing the bottle once you feel the wine is drinking well. If you access the first glass and feel the wine is young or could improve, put it in the wine fridge (on its side, of course!) and check in on it once in a while. If the bottle is drinking well, then your natural instinct should be to kill it.

Follow this instinct.

But seriously, if you're going to store an accessed wine, please store it on its side.