Why does my iptables port forward not work?

I'm trying to setup a port forwarding from port 80 to port 8080 on my amazon linux ami machine.

I ran

$ sudo /sbin/iptables -A PREROUTING -t nat -i eth0 -p tcp --dport 80 -j REDIRECT --to-port 8080

And verified the results:

$ sudo iptables --table nat --list
Chain PREROUTING (policy ACCEPT)
target     prot opt source               destination         
REDIRECT   tcp  --  anywhere             anywhere             tcp dpt:http redir ports 8080

Chain INPUT (policy ACCEPT)
target     prot opt source               destination         

Chain OUTPUT (policy ACCEPT)
target     prot opt source               destination         

Chain POSTROUTING (policy ACCEPT)
target     prot opt source               destination         

However requesting port 80 does not work:

$ wget http://localhost:80
--2017-09-25 08:51:27--  http://localhost/
Resolving localhost (localhost)... 127.0.0.1
Connecting to localhost (localhost)|127.0.0.1|:80... failed: Connection refused.

Whereas port 8080 works fine:

$ wget http://localhost:8080
--2017-09-25 08:51:39--  http://localhost:8080/
Resolving localhost (localhost)... 127.0.0.1
Connecting to localhost (localhost)|127.0.0.1|:8080... connected.

How can I let port 80 be an alias for port 8080?

Additional information:

$ cat /proc/sys/net/ipv4/ip_forward
1

$ sudo sysctl -a | grep ip_forward
net.ipv4.ip_forward = 1
net.ipv4.ip_forward_use_pmtu = 0
error: "Input/output error" reading key "net.ipv6.conf.all.stable_secret"
error: "Input/output error" reading key "net.ipv6.conf.default.stable_secret"
error: "Input/output error" reading key "net.ipv6.conf.eth0.stable_secret"
error: "Input/output error" reading key "net.ipv6.conf.lo.stable_secret"