I am German national and have been living a Germany for 30 years. I sponsored a visit visa for my sister (61) and her husband (70) living in Pakistan. Their visa was rejected and passports were sent back with these 2 objections. 
 
1:  The information provided about the purpose and conditions of the intended stay was not reliable.
2:  You intention to leave the territory of the visa countries could not be determined
 
They already visited Germany once (8 yeas ago) on my sponsorship. They has soid documents to prove there links and propertiy in home countries. I am surprised of the rejection and objections.
Can we claim again by answering the objection?  
if yes which way?

Thanks 

Your sister and her husband may file a Remonstration explaining why you think the Embassy made a mistake. I would suggest that you post your question on info4alien for more specific advice.