Cant access blog even after password change

This is an ongoing problem, that when trying to login the login page keeps coming back, and back, and back, asking for the password over and over. Then, after renewing the password, the same thing happens with That password, etc, etc, etc.

It is working from time to time, but rarely. Ususally in between days and only after dozens of tries and password changes.

Why in the world, first doesn’t something basic as a login function work on a complex blog like this (where more compex functions work flawlessly), and what could be the problem?