There are only a couple of current discontinuous roads I can think of in TX -- no, 3.
* TX 87, it's weather related. Between Port Arthur and High Island, along the coast, erosion and hurricane forces have damaged the road to where it's not recognizable or driveable any more. There's been no move to either rebuild the missing portion, nor to rearrange any of the designations of the nearest nearby roads to make up for the gap.
* TX 190, the service roads along the Carrollton-to-Garland section of the Bush Turnpike. There are no service roads east of the Kelly Blvd. exit and west of the Coit exit, and since TX 190 only exists on the service road portion, not the main lanes, and the city of Dallas didn't want service roads on it's section of the Turnpike (for some strange reason--NIMBYness, I guess), the road exists in 2 parts. And now that the Turnpike extension is done around through Rowlett to I-30 without service roads, TX 190 doesn't exist between TX 78 and I-30, either.
* TX 211, west of San Antonio. If you look up the TxDOT designation file for the road (http://www.dot.state.tx.us/tpp/hwy/sh/sh0211.htm
), it entails what was *supposed* to happen about the road. The road is actually in 2 parts currently, with the part in between a victim of NIMBYs. There was also supposed to be another part more north of the currently-built north section, according to the same designation file, but it was likely a combo-meal of more NIMBYs and $$ that hasn't brought that part to life (although I've not seen the section up close to know what any real reasons might be).
Oh, another I guess: FM 544. It once was a solid line from TX 121 east of Lewisville to the Dallas-Collin county line south of Wylie. Since then, the section within the city limits of Plano has been decommissioned, even though the city has put up signs like this (http://goo.gl/maps/ybMyZ
) almost-TX-style signage to still mark the route, seemingly to help drivers get from one end of the disconnection to the other. I'm not sure what's more strange, a town that doesn't want a designated road, leaving 2 orphaned parts; or, that the state would still keep what's left, knowing the middle part doesn't exist and the remainders have almost (not quite!) completely urbanized. Houston and Humble are perfectly fine having FM 1960, even though it's *very* urbanized, to the point of even having a quite RARE business route portion (Bus FM 1960 is an older part of the route, in the center part of Humble) along it.