In most areas crabgrass is an annual, the whole plant dies but comes back from seed the next year. According to this Texas page it is annual there:
http://aggie-horticulture.tamu...
Having said that, some people use the name for quackgrass which actually is perennial and survives below ground in the winter. So it's important to know which grass you have.
A herbicide that works well for crabgrass is Dimension if you choose to go the "chemical" route but I don't know whether it is available to homeowners in Texas or how much it costs there:
http://www.dowagro.com/turf/pr...
Well I looked it up on Amazon, not inexpensive!