Two reasons it's recently been lower:
1 - The property tax relief that the TX legislature passed a couple of years ago:
Texas Governor Rick Perry - Report of the Texas Tax Reform Commission
2 - The law in TX requires that if property taxes go up (in terms of dollars), the taxing entities must jump through some hoops and go through a public notification process. That means if appraised values of an area go up, even though the rate stays the same, the "effective" tax goes up in the eyes of state government. So, many districts have been lowering the rate rather than go through the process required for the effective tax increase.
#1 is complete now, AFAIK. So no more relief from that. #2 effectively cancels out; the higher value appraisal with the lower rate means you will end up paying the same. And many of the taxing entities will go through the public notification process eventually, so the rate may start to crank back up. Also note that this is based on overall tax revenue of the taxing entity; if your individual property jumps in value, they don't need to go through any hoops and you will end up paying more.
Similarly, if the tax appraised values go down (it's been a few years since that has happened in many areas, but it does happen) ... the tax rates are usually increased to ensure the same revenue for the taxing entities.
The best bet is to make sure your appraised value stays as low as possible -- protest your initial appraisal after purchase, if it is more than the purchase price. Then protest every year to try to reduce the increase as much as you can.