A DHCP (Dynamic Host Configuration Protocol) server is basically the phonebook of your network. It stores active numbers, spare numbers and assigns spare numbers to devices which ask for one. It's main function is to ensure all devices connected to it are on the same street but at different house numbers. Each address is leased for a set period of time, after which the address becomes available again and can be assigned to anyone who asks for one. This could be the same device or a completely new one. If it's a new device then the old device gets a new address when it reconnects, hence you get changing (dynamic) IP addresses.
Every internet router ships with an active DHCP server. You use it by default.
This is ok for a normal home network in which nobody on the internet needs to find specific things on your network. It becomes a problem if someone from beyond your "street" comes in, you always want to direct them to the same house but the tennants have changed. With your port forwarding you've created a static route to an address with changing tennants.
What do I mean by static? It does not change.
How do you mix dynamic and static addresses? With care.
How do you mix them? There are a couple of ways to do this, both of them need you to reconfigure your router. If you cannot follow the following I'll need you router make and model so I can walk you through it.
1). This depends on the capabilties of your router but is the easier method.
Navigate to DHCP/LAN setup part of you router, tick the box for the apropriate IP address/computer and select Add Reservation. This will set aside this IP address and only assign it to the LAN adapter matching the MAC address it has also stored.
Make sure this is the IP address you port forward to.
2). Again, navigate to the DHCP/LAN setup part of your router.
In it you will find "Starting IP address" and "Ending IP address"
Typically home routers work in the range 192.168.0.1 to 192.168.0.255, they will hold 192.168.0.1 for themselves and assign ip addresses starting at 192.168.0.2.
You want to raise the starting address to something like 192.168.0.10 and apply.
Log into your server, navigate to the network and sharing centre (I'll assume you're running Windows 7, but vista/server 2008/2008 r2/sbs2011 are the same)
Start -> Control Panel (Small/Large Icons view)-> Network and Sharing Centre -> Change adapter settings (link on left).
You're looking for the active adapter (they may be more than one adapter, choose one that doesn't have a cross beside it)
Double click the adapter -> Properties (button) -> Scroll down to "Internet Protocol Version 4 (TCP/IPv4)" -> Highlight it and click properties
In the new window you are about to assign a static IP address.
Click the "Use the following IP address:" radio button.
Enter information
IP address: 192.168.0.5 (something just beyond the range of the dhcp server, the first three parts must match it though)
Subnet mask: 255.255.255.0
Default Gateway: 192.168.0.1 (or whatever IP address your router is at)
Further down you will also need to assign a DNS server address.
Preferred DNS server: 192.168.0.1
Hit OK or cancel all the way out.
Go back to your router and port forward to you server's IP addfress.
Done
Notes:-Throughout I have assumed your router is set for the IP address range starting 192.168.0.x. If this is not the case please replace it with whatever your router does start with, this could be 10.10.1.x or 192.168.1.x.