User password valid only for one day
Finally the problem in my case had to do with the text that was sent with mail after user registration. When user was registered a mail was sent in his inbox with his username and a (system created) password. Then the text was providing a link to the login page, a second one linking to the auto log in page (where the user supposedly would not have to enter his password) and a third one that it is irrelevant. 

So i realized that the second link was actually a link to reset your password if you forget the old one. So the user when first reading the mail he click on the second link to log in automatically but he doesn't know that the password given to him was reseted and now his log in was valid only for one day or for one use. Each time he has to reset his password.

Anyway if you have access to your database you can experiment to see if it is another issue for you. You can create a fake account in drupal. In the mail that is sent to you click the second link (something like http://mysite.com/foo/user/reset/1085/1349294892/7bc9baf9d42aa774be00a0f36090323f). Then go to table 'user' of the drupal database, find the fake user you created and modify the record of the column 'created'  and put a unix-timestamp older than a day (there are online unix-timestamp creator). This way you can experiment if the password is temporary or not.