For all interested parties:
"Visit Visa Extensions" can now be done online at
http://www.moi.gov.sa/wps/portal/moi/eservices
Conditions:
1. you must be registered on "Abshir"
2. extension fee must be paid before following the online process.
After many hours over the last 2 days at Jawazaat Riyadh, I successfully extended a family members visit visa using this service.