In order to enable online learning to continue developing when the COVID-19 pandemic passes, this study aimed to identify the critical factors that affected the use of e-learning by university students during the pandemic. These critical factors will help to increase the efficiency of future development and deployment of online learning systems. Through a literature review, this study employed the technology acceptance model, social support, and task–technology fit as the theoretical basis to establish the framework of the online learning environment with regards to the technology acceptance model in the context of emergency management. A questionnaire survey was administered to students in universities that had implemented online teaching during the pandemic, and 552 valid responses were collected. The survey explored the factors affecting the willingness of higher education institution students to continue using online learning, and the following conclusions were drawn. (1) The easier an online learning platform was to navigate, the better it was perceived by the students, and thus the students were more willing to use it. (2) Ease of use and usefulness were associated with the teachers’ choice of platform and their ability to achieve a satisfactory fit between the course design and platform navigation, which thereby affected the students’ learning outcomes and attitude towards use. (3) The positive attitude of teachers towards teaching increased the students’ perceived ease of use of online learning. (4) During the pandemic, family support—a major support for teachers in online teaching—enhanced teachers’ attitudes towards, and willingness to provide, online teaching. A high level of support showed that the parents urged the students to learn and complete online learning tasks as instructed by the teachers, implying that family support could affect the students’ habits towards, adaptation to, and identification of online learning. The study results provide insights into the factors affecting the willingness of teachers and students to continue using e-learning platforms.