As a long-time chorister, I've always wondered what drives choirs to flat or sharp out of certain keys. For instance, the choir I sing with consistently fails to remain in the key of F, whereas shifting the music to F# fixes our tonality issues instantly.
If you're absolutely sure that this is occurring, I'd guess it has something to do with the voices of the singers in your particular choir: there are areas called "breaks" in the human voice, and around those particular pitches, it can be easy to allow yourself to slip flat or sharp. I suspect the pieces you're singing stay close to some singers' breaks, and shifting the key is moving the pitches in a way that causes them to fall cleanly into one area of the voice or another, reducing the tendency to fall out of tune.
But this seems very unlikely. It could be psychological--changing to an unfamiliar key could cause the singers to listen more closely. I'd be surprised if this phenomenon arose in a controlled experimental environment.