Where does “непогрешимый” come from?

непогрешимый (Russian) comes from Russian не-, from Russian не, from Proto-Slavic ne, from Proto-Balto-Slavic nē, from Proto-Indo-European né — not; no.

Ancestry of “непогрешимый”, step by step

Step	Language	Word	Meaning
1	Russian	не-	un-, non-, in-, im-, ir-, dis-, mis-
2	Russian	не	not, no, -n't, without; Idiomatic negative usage;...
3	Proto-Slavic	ne	not
4	Proto-Balto-Slavic	nē	—
5	Proto-Indo-European	né	not; no

Every word from Proto-Indo-European né →

непогрешимый — Etymology, Origin & Word History | Etymology Explorer