You're trying to connect to a SQL Server, and it is taking longer than ADO.NET is willing to wait.
Try connecting to the same server, using the same username and password, using SQL Server Management Studio. If you get the same error, there is either something wrong with your connection string, the server you specify is not running, or you can't get to the server across the network from where you are (maybe you're on a public IP address trying to get in to an internal server name). I can't think of a scenario in which you'd enter the exact same server and credentials into SSMS and connect, then do the same in ADO.NET and fail.
If you're on a slow network, you can try increasing the timeout value. However, if a connection is going to happen at all, it should happen pretty quickly.
Take a look at both your SQL Native Client settings, and the SQL Server settings on the server. There is a section for allowed protocols; SQL can connect using a variety of protocols. Usually, you want TCP/IP for a server on the network, and Named Pipes for a server running on your own computer.
EDIT FROM YOUR COMMENT: Oh, that's normal; happens all the time. From time to time on a TCP network, packets "collide", or are "lost" in transmission. It's a known weakness of packet-switching technologies, which is managed by the TCP protocol itself in most cases. One case in which it isn't easily detected is when the initial request for a connection is lost in the shuffle. In that case, the server doesn't know there was a request, and the client didn't know their request wasn't received. So, all the client can do is give up.
To make your program more robust, all you have to do is expect a failure or two, and simply re-try your request. Here's a basic algorithm to do that:
SqlDataAdapter sqlClearQuestDefects;
short retries = 0;
while(true)
{
try
{
sqlClearQuestDefects = new SqlDataAdapter(sql, "Data Source=ab;Initial Catalog=ac;User ID=ad; Password =aa");
break;
}
catch(Exception)
{
retries++;
//will try a total of three times before giving up
if(retries >2) throw;
}
}