redis master slave replication stopped working

I'm trying to figure out how to troubleshoot my redis master / slave replication. It has "just stopped" working.

Setup Information

Let's say my master's IP address is 10.1.2.3

Here's what I've checked so far:

1. I've restarted redis on both the master and slave... but anytime I run INFO REPLICATION on the slave it shows the link as "down"

2. Ran netstat -lnp on both the master and slave. Here's the output from the master:

masterdb:~# netstat -lnp | grep 6379
tcp        0      0 127.0.0.1:6379          0.0.0.0:*               LISTEN      21611/redis-server
tcp        0      0 10.1.2.3:6379      0.0.0.0:*               LISTEN      21611/redis-server

And from the slave machine:

slavedb:~# netstat -lnp | grep 6379
tcp        0      0 0.0.0.0:6379            0.0.0.0:*               LISTEN      5577/redis-server
tcp        0      0 :::6379                 :::*                    LISTEN      5577/redis-server
slavedb:~#

3. I've checked the logs on both the master and the slave and I don't see any error messages. But I see timeout messages on the slave... which I think I've seen before, even when replication was working. The log looks like this on the slave:

5577:S 26 Oct 13:17:19.510 * MASTER <-> SLAVE sync started
5577:S 26 Oct 13:18:20.597 # Timeout connecting to the MASTER...
5577:S 26 Oct 13:18:20.597 * Connecting to MASTER 10.1.2.3:6379
5577:S 26 Oct 13:18:20.597 * MASTER <-> SLAVE sync started
5577:S 26 Oct 13:19:21.685 # Timeout connecting to the MASTER...

4. When i start the redis-cli on the slave and re-issue the slaveof command, i get this message:

   127.0.0.1:6379> slaveof 10.1.2.3 6379 OK Already connected to specified master 127.0.0.1:6379>

5. I also tried the following commands on the master :

127.0.0.1:6379> save
OK
127.0.0.1:6379> bgsave
Background saving started
127.0.0.1:6379>

But that didn't resolve anything on the slave. It still says the link is down when I check the INFO on REPLCIATION:

   127.0.0.1:6379> info replication
    # Replication
    role:slave
    master_host:10.1.2.3
    master_port:6379
    master_link_status:down
    master_last_io_seconds_ago:-1
    master_sync_in_progress:0
    slave_repl_offset:1
    master_link_down_since_seconds:1477488462
    slave_priority:100
    slave_read_only:1
    connected_slaves:0
    master_repl_offset:0
    repl_backlog_active:0
    repl_backlog_size:1048576
    repl_backlog_first_byte_offset:0
    repl_backlog_histlen:0
    127.0.0.1:6379>

I'm not sure what else to check.