The problem is likely not with the static or dynamic IP, but because you have two routers doing NAT, the first being the modem/router your ISP gave you and the second being the Airport Extreme.
What happens is your ISP assigns your modem an IP address, this can either be a different one every time you connect (or say every few months) the modem which is a dynamic IP, or they always assign you the same IP address in which case it is static.
Your ISP's provided modem/router then uses NAT to share that single IP it has been assigned by the ISP to any other devices connected to it, by using DHCP to assign them a private IP address which would be in one of the ranges 192.168.x.x, 172.16-31.x.x or 10.x.x.x.
You then connected an Airport Extreme which is also a router, so it takes the private IP assigned to it by the ISP provided modem/router and then uses NAT to share that single IP to any other devices connected to it, by using DHCP to assign them a private IP address. Unless you set it up in bridge mode which turns off its DHCP and NAT capabilities.
So you need to either:-
A) Harder Way. Set the ISP's modem/router to bridge mode, setup the Airport Extreme to handle the connection using PPPoE. The Airport Extreme now handles the NAT and DHCP. You then only need to adjust the firewall/open the ports on the Airport Extreme. This is likely the harder way of doing it as the ISP's modem/router may not be easily set to bridge mode. Only the Airport Extreme can be connected to the ISP's modem/router.
B) Easier Way. You set the Airport Extreme to bridge mode, it is then assigned a private IP address by the modem/router your ISP gave to you. Any devices connected to either the Airport Extreme or your ISP's modem/router is assigned private IP addresses by the ISP's modem/router's DHCP server. You only need to adjust the firewall/open the ports on the ISP's modem/router, as the Airport Extreme just passes anything through. This would be the easier setup.