I had a situation with DL last year where my daughter was supposed to catch a flight at 8 am. They called and said that due to some mechanical difficulty or other, the ETA was now 3 pm! They also apologetically told me that if the issue was resolved, the plane could leave at any time and she should go to the airport and wait, or risk missing her flight and not be compensated. The only other rerouting was quite complicated and involved lengthy connection but I took it. Once they have a delay, you really take a risk if you leave the gate area - they can and will push off with little notice.