If you are being asked to enter your login information each time you attempt to access a Yahoo! mobile webpage, either:

Your mobile web browser is automatically deleting cookies:
Your login information is retained by a cookie that is saved by your mobile web browser. If this cookie is deleted, you will be asked to sign in the next time you visit the page. Some mobile web browsers clear cookies and other cached information each time the browser is closed or the device is powered down. To resolve this, turn off this function in your mobile web browser.

Your login cookie has become corrupted:
If the cookie storing your login information has become corrupted, you will need to clear your mobile web browser's cache and cookies.

Note: Please refer to your phone's OS help or operation manual to get the exact steps to perform these functions as steps vary between mobile devices and mobile web browser applications.