Fix login function on my website

I have a website ([[login to view URL]][1]) that provides 30-day free trading signals in stocks and commodities. And it also has paid subscriptions in stocks and commodities. Both sets of signals are provided after the client "logs in" with a user name and password. Someone signing up for the free signals enters his email address and the site automatically sends him back a password to access the free signals for 30 days. Lately, the user name (email address) and the password we provide works for a few days, then it stops working and when the client tries to login he gets a "change password" screen that doesn't work. I want someone to investigate the problem and fix it.