Conntrack module remembers recent connections for X seconds before they finally expire. This, in my understanding, is because iptables has several other modules that can utilize this information: for example, if you want to ban some IP address if it makes X new connections during some time frame.
netstat, on the other hand, shows real-time information and is not interested about ancient history.
Have you increased maximum amount of entries in conntrack table? With a recent-ish kernel, what does
... or with some older kernel,
return to you? You may raise that value permanently via
/etc/sysctl.conf or temporarily (until next reboot) via
sysctl -w net.ipv4.ip_conntrack_max