Finally solved this with the IBM support.
This was due to the fact that our DB2 is installed in french language and that the script /usr/sbin/rsct/sapolicies/db2/db2V97_start.ksh
is trying to grep "Database name" but on our system we have "Nom de la base de données".
So the script part going like this :
su - ${DB2INSTANCE?} -c "db2 list database directory" | grep "Database name" \
| tr "[a-z]" "[A-Z]" | awk '{print $4}' > ${dbFN?}
has to be changed into this :
su - ${DB2INSTANCE?} -c "db2 list database directory" | grep "Nom de la base de donn" \
| tr "[a-z]" "[A-Z]" | awk '{print $8}' > ${dbFN?}
I didn't write the end of the word données because it doesn't work. I guess it's a problem with the encoding on our server, fr_FR@euro.
This has been tested on both v9.7 fixpack 5 and 6.
And to answer my question, the "standby" node is reintegrated to the HADR cluster automatically if it's powered off and is powered on after that while the primary node has no issue.