Why are Java Timer threads disappearing?

I have code that schedules one-time tasks to execute and does this over and over. It looks something like this.

public static void main(String[] args) 
{
    while(true)
    {
    ....
    TimerTask closeTask = new CloseTask(cli);
    Timer timer = new Timer(true);
    timer.schedule(closeTask, (long) (iPeriod * 60 * 1000));
    ...
    }
}   
public class CloseTask extends TimerTask 
{
    Client client;
    CloseTask(Client in_client)
    {
        client = in_client;
    }
    public void run()
    {       
        try
        {           
            for(int iRetries = 0; state == OPEN; iRetries++)
            {                   
                logger.log_trade_line_grablock( "Thread " + Thread.currentThread().getId() + ": About to send message", true, true, true, true, true);
                client.send_mesg("close");
                logger.log_trade_line_grablock( "Waiting 5 seconds before retrying ", true, true, true, true, true);
                Thread.sleep(5000);
            }
        } 
        catch (Exception e)
        {
            e.printStackTrace();
        }
    }   
}

The intent of the run() method in the CloseTask class is to loop until the state variable changes from OPEN state to something else. However, intermittently the timer threads simply disappear, while state still equals OPEN, which I know by printing out all the thread ID's of the currently running threads every 5 minutes.

So my questions: 1) The only explanation I can think of is that the CloseTask object is throwing uncaught exceptions. Is that correct? 2) If 1) is correct why isn't my try catch block catching these exceptions? 3) If 1) is correct is there a way to catch these exception that slip through uncaught?

Thanks for any insight into this issue.