I think if enough time has passed (e.g. 1+ years) that feelings have chilled and you both have moved on romantically, sure, why not*. But the moment you start to feel like you have to hide it or things start to get the wrong kind of intimate (as any other emotional affair), then they have to go.

Edit: *although I'm thinking more about a chat on social media every now and then, or meeting in a group every now and then, not meeting weekly/daily just the two of them.