The AP is connected through HyperTerminal and has a Wired LAN cable in the Ethernet port. When I reset the AP I gain an IP from DHCP but when I want to give it a Static IP I cannot do this as I loose connection.
How can I force it to accept a Static IP and keep this setting?
As with any Cisco equipment, you need to save the configuation otherwise it will be lost on reboot. Use the command write memory or copy running-config startup-config from the enable prompt to save the config. You can abbreviate the commands if you don't want to type the whole thing.
Cisco AP1200 IOS 
Linear Mode
