Symptom: After you replace your SSL certificates on your ADFS servers you continue to receive the following alert inside of the Office 365 portal.

Renew your certificates
One of your on-premises Federation Service certificates is expiring.  Failure to renew the certificate and update trust properties within XX days will result in a loss of access to all Office 365 services for all users.  Update now

Solution: This error can be caused if any of the three primary SSL Certificates that are required to federate to an external identity are nearing their experation date (Service Communications, Token-decrpting, and Token-signing).

Verify which SSL certificate is about to expire

1. Login to your primary ADFS server
2. Open up Server Manager
   
3. Select Tools -> AD FS Management
   
4. Under AD FS expand Service and select Certificates
   
   
5. Verify if any certificates are set to expire
   1. Note: In this case, you can see the Token-decrypting and Token-signing certificates are set to expire soon

Replace the expir(ed)(ing) certificates

Unfortunately, I don't currently have a tutorial on the processes behind replacing each certificate.  The process for replacing each certificate is a tad different.  Here are a few articles that might help you:

Replacing the Service Communication certificate: http://blogs.technet.com/b/tune_in_to_windows_intune/archive/2013/11/13/replace-certificates-on-adfs-3-0.aspx

Replacing the token-signing and token-decrypting certificates can be found here: http://social.technet.microsoft.com/wiki/contents/articles/2554.ad-fs-2-0-how-to-replace-the-ssl-service-communications-token-signing-and-token-decrypting-certificates.aspx#Replacing_the_Token-Signing_certificate

Update the federated trust with Office 365

1. Once your certificates are not nearing their experation date, open up the Windows Azure Active Direcotry Module for Windows PowerShell as an administrator
   1. Note: Installation instructions and the download for this can be found here: http://technet.microsoft.com/en-us/library/jj151815.aspx
      
2. Execute the following command
   1.  Connect-MsolService
      
      1. Note: Enter in your Office 365 administrator credentials on this step
3. Execute the following command
   1. Update-MsolFederatedDomain -DomainName mydomain.com -SupportMultiDomain
      
      1. Note: Replace mydomain.com with your federated domain.  If you have multiple domains you are federating with Office 365, add the optional -SupportMultiDomain paramter as well