The Rebbe's guidance to those living in Eretz Yisrael who consider leaving, even temporarily:
Only for a serious reason. Leaving Eretz Yisrael is restricted by halachah and should be considered only for very serious reasons (IK 9829, 9995); if there is any doubt, don't leave (IK 10551, 10885). The Torah's obligation here doesn't change with circumstances (IK 9342). Consult a halachic authority before relocating abroad for work (IK 9287), and weigh any departure by Torah guidelines (IK 7657).
For Torah study. Leaving for Torah study is permitted only when it brings a clear improvement in one's learning, by both halachic and chassidic standards (IK 2257, 4061); travel from Eretz Yisrael is allowed for Torah study, and afterwards one should return (IK 9989). Supporting sincere students who wish to learn abroad brings blessing (IK 9828).
Stay and grow where you are. Remain in Eretz Yisrael for Torah study and communal work rather than travel unnecessarily (IK 1145, 2038), even when you feel your opportunities there are limited (IK 2558). Weigh each trip by its effect on your spiritual growth (IK 10820). The Rebbe often advised residents of Kfar Chabad to stay rather than move or travel abroad (IK 9720).
See also: Land of Israel – Making aliyah; Land of Israel – Living in the Holy Land.