I am sure as long as there are suckers (i.e. the US taxpayers) willing to fund such experiments that there will be no shortage of people willing to try to achieve time travel. Doesn't matter that it is impossible in our physical realm, it will be tried never the less for something much more practical, money.
I not saying in the supernatural realm that time travel is impossible, (e.g. God can freely visit any point in time that he chooses) but it is in our realm, and it always will be.