Question: Since the beginning of Covid, we have been davening in different rooms in our shul. One of these rooms has an aron hakodesh but for security reasons, the sefer torah is removed on days when there is no leining. When saying tachanun on those days, should we not put our head down on our arms?
Answer: The Gemara (Megilla 22b, Bava Metzia 59b) teaches us that people would prostrate themselves (nefilas apayim) as part of their davening. The Shulchan Aruch (OC 139:1) writes that nowadays we bow our heads and rest them on our arm. (See Aruch Hashulchan OC 131:4)
The Rema (OC 131:2) quotes the Rokeach (324) who writes that nefilas apayim is not practiced unless one is in the presence of an aron hakodesh and sefer Torah. This is alluded to in the incident of Yehoshua (7:6) at the battle of Ai, when Yehoshua fell on his face in front of the aron hakodesh. The Mishna Berura (131:11) writes that this applies equally if there is a sefer Torah without an aron hakodesh (See Teshuvos Vehanhagos 2:79).
The Aruch Hashulchan (OC 131:10) explains why the Shulchan Aruch does not record this halacha. The original source for nefilas apayim is when Moshe describes falling on his face on Har Sinai after breaking the first luchos. He did so, even though there was no sefer Torah present. Nonetheless, he writes that we follow the Rokeach and Rema and only perform nefilas apayim in the presence of a sefer Torah.
R’ Shlomo Zalaman Auerbach (quoted in Ishei Yisrael 25:n37) maintained that if one removed the sifrei Torah to a safe, one would still perform nefilas apayim when the aron hakodesh was empty. R’ Moshe Feinstein (Igros Moshe OC 4:21:1) stresses the importance of keeping the sifrei Torah in a secured safe.
In conclusion, one performs nefilas apayim while reciting tachanun, even if the sefer torah was removed to a more secure location.