Problem with database connections timing out for long-running queries

I'm running into a problem where the connection between application its
database is timing out after 12 hours.

Here's the context:

. Two servers (one running the application and another hosting the
database) in the Amazon AWS environment on different subnets within a
virtual private cloud

. The server hosting the application is running Ubuntu 14.04.2 LTS

. The server hosting the database is running Ubuntu 14.04.2 LTS and
PostgreSQL version 9.4.4

. An stunnel connection is provisioned from the client to the
database. The app server is running stunnel version 4.53 with the following
stunnel.conf settings:

; PID is created inside the chroot jail

pid = /stunnel4.pid

[postgres-<host>]

client = yes

protocol = pgsql

accept = 5432

connect = <host>:5432

options = NO_TICKET

retry = yes

. The database is provisioned to only accept "hostssl" type
connections from the application server

I've enabled the logging of PostgreSQL connections and disconnections and I
see that for connections that terminate before the associated query
completes, the session time shown in the disconnect message is 12 hours plus
three or four seconds.

I see this problem with both of the default tcp_keepalives settings of:

#tcp_keepalives_idle = 0

#tcp_keepalives_interval = 0

#tcp_keepalives_count = 0

And with the following settings:

tcp_keepalives_idle = 120

tcp_keepalives_interval = 120

tcp_keepalives_count = 5

I don't see the disconnect problem for long-running queries that use a local
database connection.

Any advice on what might be causing remote database connections to drop
after 12 hours (and how to work around the issue)?

Kind regards,
Rich