That sample is called a panel. A researcher could, for example, select a sample of UT graduate students, and ask them questions on their library usage. Every year thereafter, the researcher would contact the same people, and ask them similar questions, and ask them the reasons for any changes in their habits. Panel studies, while they can yield extremely specific and useful explanations, can be difficult to conduct. They tend to be expensive, they take a lot of time, and they suffer from high attrition rates.
Attrition is what occurs when people drop out of the study.
Surveys should be just as rigourously designed and administered as any other research method. A sample is representative when it is an accurate proportional representation of the population under study. If you want to study the attitudes of UT students regarding library services, it would not be enough to interview every 100th person who walked into the library. That technique would only measure the attitudes of UT students who use the library, not those who do not. In addition, it would only measure the attitudes of UT students who happened to use the library during the time you were collecting data.