No feedback despite numerous emails to customer services over almost 3 months!!!!!

My two children and I missed our connection flight to Cape Town at Frankfurt airport on the 19th of July 2017 due to our flight from Sweden being delayed. Due to all flights to Cape Town already being fully booked for the next few days we ended arriving back home 3 days later then expected (flying out via Munich in the end). Unfortunately (no fault of Lufthansa of course) we also had the misfortune that my youngest son got very ill during our brief stay in Germany and ended up getting admitted to hospital for a night. I was hoping that Lufthansa might be able to pay me some compensation for our substantial delay and I sent my first e-mail to Lufthansa customer relations on 29th of July 2017. I received an automated response and a case number but nothing else. I have since sent six more emails referring to my case number but not had a single response. I have also tried to call them and sat on hold to a German number for over 45 minutes before giving up. I find it totally shocking that such a big company provide NO CUSTOMER CARE AT ALL!!!!