You can use awk with custom field separator:
s='A1_KOG1494_________AAMFAARSFSERK'
awk -F '_{2,}' '{print $2}' <<< "$s"
AAMFAARSFSERK
awk -F '_' '{print $NF}' <<< "$s"
AAMFAARSFSERK
Another example:
awk -F '_{2,}' '{print $2}' <<< "A3_KOG1494___________AAKFALRSFSCCK"
AAKFALRSFSCCK