On an '07 the light would blink for a few seconds and then go solid when the BCM does not get a signal from a sensor. The '04 to '06 worked slightly different so I'm not sure if it is a dead sensor or if the BCM is acting up. If you get the Nissan Service Manual for '06 models it should tell you what the light is trying to say.
My research showed that a typical TPMS sensor had an expected lifespan of 7 to 10 years. That's only because the battery is not one you can replace. So when the battery dies the entire sensor is considered to be scrap. Since you got 11 years out of yours you are a real over achiever.
You could go to Discount Tire and they can figure out which sensor is bad and replace just that sensor. However, if one failed, the rest aren't far behind. The sensors that Discount Tire sells will work with the Titan system. I have two sets of wheels/tires with sensors from Discount Tire.