Documented information on quality objectives for HSE department was not maintained. what might be the possible root cause for this.
First question: Were there quality objectives established?
If yes, were the quality objectives kept up to date? It sounds like no.
So the next question would be why not, who was/is responsible to maintain these objectives?
Is there a reason why they did not maintain the data?
After drilling down this reason, you can ask additional questions. Does anyone actually care about this data or is it 'useless data'. I would look into this as a secondary effect as not having the quality objectives updated and no one notices, to me, means no one actually uses the data. Looking into if anyone uses the data does not address the root cause, in the case of the root cause you (the company) said you were going to use these objectives and maintain them and you did not. Finding out that you do not use the data comes after answering the corrective action as continuous improvement.