A friend had this issue and it was a bizarre similar story. Everytime they enabled security, drops. I happened by and looking at the connection list on the router there was an uninvited user. We tried turning on MAC filters and they would get kicked off. In 5 minutes another user would attach hijacking the MAC address we had allowed. This was not a good sign.
While WPA would drop my theory was the person who was pilfering the wifi was likely the source of the trouble. My advice was to switch to wpa/wpa2 and live with the drops until they gave up.
About a week later the drops stopped so we bet they moved on.
This is not to say this is your issue.
I have a strange connectivity problem which I've tried through two different WiFi routers:
My WiFi router is connected to my Cable modem. Whenever security is enabled on the router (be it WPA, WPA2 or WEP), the connections between my WiFi router and client devices frequently drop (i.e., iBook, iPhone, Mac Pro) so that I cannot get email, etc. It's only (temporarily) solved by turning the Airport card off and on again. (Note: the signal from the router is okay-- just the connectivity drops.)
Connection Doctor on my Mac shows that the Configuration is changed/reset on OSX. Other diag codes on different apps signify "Server Timeout," etc.
Is there something else I need to configure on my router? Or turn the OSX firewall off?
Any advice appreciated.