I have been using the same DB connection string for a long time and not have issues.
Suddenly, I have troubles logging in to any */web pages, and when on jts/admin I get errors saying
"Service Temporarily Unavailable - The Server is temporarily unavailable to service your request due to maintenance downtime or capacity problems.  Please try again later."

When I look in the jts.log, I see the following error:

2016-04-11 11:27:07,121 [              WebContainer : 5] ERROR com.ibm.team.repository                             - CRJAZ2654E The server was unable to connect to the database because the database connection syntax is invalid. Verify the syntax in your teamserver.properties file. See the Jazz Team Server log for more information.
com.microsoft.sqlserver.jdbc.SQLServerException: The driver could not establish a secure connection to SQL Server by using Secure Sockets Layer (SSL) encryption. Error: "SQL Server did not return a response. The connection has been closed.".

I confirmed that the timestamp from teamserver.properties is old and that there have not been any changes to the credentials for the DB.

The only changes to the server was a security/encryption update.