Landlords in Texas are required to repair problems that materially "affect the physical health or safety of an ordinary tenant" according to property code 92.056, which is the state's version of the implied warranty of habitability. Unfortunately, the law doesn't go into any more detail than that so you'll have to use your best judgement.
One detail regarding your landlord's responsibilities that Texas law does cover is hot water. Any problem arising from a landlord's failure to provide a hot water supply at a minimum of 120°F is a breach of the warranty.
If you're wondering about a repair that might not affect your health clearly, take a look at your lease agreement. It likely covers appliance repair or other, less serious, fixes.
The information provided on this website does not, and is not intended to, constitute legal advice.