How do you upgrade a MongoDB replica set backing a Meteor app without Meteor app downtime?

The MongoDB Cloud Manager (web GUI for managing MongoDB clusters) has a nice one-click upgrade feature. I can just use a dropdown to change a replica set’s version, and it takes care of the rest. The problem is, every time I use it my Meteor apps freak out and fail to reconnect. I don’t have all the information yet, but it might be code running, for example, from Meteor.setInterval().

Typical errors seen: Error: No replica set member available for query with ReadPreference undefined and tags undefined.

Anyone else have similar issues with MongoDB replica sets? Do companies like Compose just take care of this for you so apps never notice the downtime? Do I need something in front of my mongod processes?