Can a beef brisket be tenderized by cooking a second time?
Yes, you can cook it a second time and it may help. When you cook meat two things will happen (well, more than two...). 

One is that it will lose moisture. The longer you cook it the more moisture (i.e. water) you will lose, and there's no getting it back. 

The second thing that happens is that the connective tissues break down to collagen, which is what you are perceiving as being moist and tender when you cook it for a long time. If it is cooked but not to the point where these connective tissues break down then it is likely a second cook will make it more tender. It will also continue to dry out the meat.  

After your second cook, be sure to let it rest. I would also suggest slicing it thinly against the grain after cooking as this will make it easier to chew, further helping with the mouthfeel. 

Finally, be aware that the amount of time the meat stays between 40°F-140°F the more risk there is of food poisoning. Cooking a second time does not eliminate any toxins produced by the bacteria up to that point (it will only kill bacteria), so be sure to eat it right away as letting it cool and reheating it again introduces more risk. Guidelines say meat should be kept for only one hour between 90°-140° (up to four hours 40°-90°, but less depending how much time was spent above 90°).