Connecting to an external database with pgAdmin III

Question

I'm trying to connect to an external database from pgAdmin III (which is installed on both machines). The client complains:

Access to database denied

The server doesn't grant access to the database: the server reports

FATAL: no pg_hba.conf entry for host "192.168.108.161",
                                user "postgres",
                            database "postgres",
                                 SSL off 

To access a database on a PostgreSQL server, you first have to grant primary access to the server for your client (Host Based Authentication). PostgreSQL will check the pg_hba.conf file if a pattern that matches your client address / username / database is present and enabled before any SQL GRANT access control lists are evaluated.

The initial settings in pg_hba.conf are quite restrictive, in order to avoid unwanted security holes caused by unreviewed but mandatory system settings. You'll probably want to add something like

host all all 192.168.0.0/24 md5 

This example grants MD5 encrypted password access to all databases to all users on the private network 192.168.0.0/24. You can use the pg_hba.conf editor that is built into pgAdmin III to edit the pg_hba.conf configuration file.

After changing pg_hba.conf, you need to trigger a server configuration reload using pg_ctl or by stopping and restarting the server process.

Where the server explicitly states that all connections from the internal network are accepted.

pg_hba.conf

# TYPE  DATABASE        USER            ADDRESS                 METHOD
# "local" is for Unix domain socket connections only
local   all             all                                     md5
host    all             all             127.0.0.1/32            md5
host    all             all             ::1/128                 md5
host    all             all             192.168.0.0/24          md5

I have already restarted the postmaster for the changes to take effect, and have gone so far as to restart the entire machine. What else could be going wrong here?