When you are publishing a requirement to an applicant, you are publishing it to a specific applicant account. The account where a requirement has been published to can be seen in the Applicant Account field of a requirement's Online section. To view the email address in this field, click Show next to the field to see the account a requirement has been published to.
The next question is: what is the email address of the account that the applicant is logging in to? Is it the same, or is it different than what is in applicant account? If it is different, 1 of 2 things should happen
1. The applicant should log in to the account shown in applicant account
2. You can delete the requirement from the web and publish it out again, making sure it is going to the account the applicant is logging in to.