Modulus deploy downtime

I have two environments hosted on Modulus: Staging and production for the same app.
This means that the code is identical - only the amount of users and the contents in the two DBs are different.

But the downtime after deployment is vastly different! My staging environment is live again after a few seconds, but the production environment takes almost 2 minutes to come alive. And since there’s no possibility to specify a static maintenance page with Modulus, my users are just presented with the dreaded “Unable to connect to any application instances.” for the entire time.

That’s not acceptable, but I have no idea how to debug or fix this.
Does anyone know what’s going on that could cause the wait?