It most likely has to do with cookies. Is there a setting in your router's Admin for page refresh rate? What I think is happening is that when the Admin page refreshes, it can't find the login credentials(cookies) for your router. And so you keep getting the login prompt.
Check to make sure cookies are allowed to be set in your browser. Otherwise, make an exception to allow for cookies at 192.168.1.1, your router's IP address(default gateway).
You might be able to remove the password which would allow directly logging into your router Admin from a bookmark. But, if anyone hacks into your WiFi signal, they could easily access the Admin page. Which would allow them to change all passwords to the router and WiFi, and require a hardware reset to reconfigure your router settings. Still only a small chance if using a strong encryption and password for WiFi access.
I use Firefox and the extension
Secure Login which allows one-click access to all my routers and websites.
BTW, I've done some limited testing of Firefox password database, and was not able to capture any using a few popular keyloggers. So comfortable that it's a secure method of password storage, as long as the browser is kept updated, and no vulnerabilities are exposed. I've also hardened the password database itself using Truecrypt.
