> 1) Is this the expected behaviour ?
No, it is not. I never have to do this.
> 2) Is it safe to enter the "enable configuration" every time I see this warning ?
Yes. Doing so won't cause any harm.
> 3) Could there exist an underlying problem which we might have overlooked ?
Yes. But then I think this answer is obvious since I replied "No" to question 1. I would start by looking in $DIAGNOSTIC_DEST/diag/rdbms/admin/db_name/instance_name/trace for the DG Broker log file (named drcinstance_name.log). Look to see if there are clues as to they the broker config was disabled around the time of shutdown or startup.
I would also consider filing a SR with Oracle Support on the issue.