In theory, it is possible to land a spacecraft on the moon and have it stay there for an extended period of time, if not indefinitely. In fact, several spacecraft have been intentionally landed on the moon and remain there to this day.
The most famous examples are the Apollo Lunar Modules from the Apollo missions conducted by NASA in the 1960s and 1970s. These modules served as the landing craft for astronauts and were left on the moon's surface after the astronauts returned to Earth. They continue to remain on the moon as a testament to human exploration.
Additionally, various unmanned missions from different countries have landed spacecraft on the moon. For example, the Chinese Chang'e missions have successfully deployed landers and rovers that have operated on the lunar surface for extended periods.
The key to having a spacecraft remain on the moon for an extended period lies in its design, construction, and mission objectives. Factors such as power supply, communication systems, thermal management, and durability need to be considered to ensure the spacecraft can withstand the harsh lunar environment.
That being said, nothing is truly permanent or eternal, and even spacecraft left on the moon will eventually be subject to the effects of micrometeorite impacts, lunar dust, temperature fluctuations, and other environmental factors over an extremely long time span.
Nevertheless, with careful planning and engineering, it is possible to land a spacecraft on the moon and have it stay there for an extended duration, contributing to scientific exploration and understanding of Earth's natural satellite.