It seems there is a machlokes among the rabbonim whether the yeshiva boys learning in cities and towns around southern Israel, in range of the rockets, should stay put and continue learning or relocate to towns farther north, outside of the range of the rockets.

Rav Chaim Kanievsky has so far said that in the meantime the yeshiva boys should stay put and continue learning in their southern cities, as well as increasing their davening and saying tehillim. At the same time, he told a resident of the south who happened to be in central Israel that he need not return to his house until things calm down.
source: Kikar and Bechadrei

if you are there do not leave, but no reason to go and put yourself in danger.

Despite Rav Kanievsky's psak, some yeshivot and yeshiva boys are packing up for safer locations farther north. Gur has moved the yeshiva in Ashdod to the beis medrash in Jerusalem. Rav Shteinman told a yeshiva in Ashdod to relocate for now to a yeshiva in Karmiel. Rav Shteinman also told another southern yeshiva to move, and they will go to Bnei Braq. Belz is also moving its yeshivas in the south to Jerusalem. Rav Shmuel Auerbach seems to agree with Rav Shteinman on this one and told the Grodna yeshiva affiliated with him to move from Ashdod for now.
Vizhnitz is, for now, staying put in Ashdod.
source: Kikar and Kooker

I have yet to see a yeshiva named that is following the directive of Rav Kanievsky.

Srugim calls the Haredi community "ketanei emuna" - men of little faith, due to their largely abandoning the south in these troubled times. They point to the hesder yeshivas and other DL yeshivot that are all staying put and continuing to learn on their regular schedules.

I dont think "little faith" is a good categorization. They might be leaving because of little faith and being afraid of the danger, but they also might be leaving because the rockets are causing too much of a disruption in their learning. If they arent able to focus and learn properly, it surely must harm the level of protection their learning would otherwise offer to the southern communities, and to themselves. By moving, they will be able to focus and learn again and provide their protection - anyways, who says they protect specifically the areas immediately around them? they should be able to provide protection from central Israel as well!

Another theory is that perhaps their protection, in these dire times, is more needed in important cities like Jerusalem and Bnei Braq than in small towns and cities like Ashdod, Sderot and Beit Chilkiya...