I have a domain and sub-domain each one on the different server. I want to know is it possible that the down-time of the main domain effects the functionality of sub-domain which is on the different server.
Since both your domain (example.com) and your subdomain (sub.example.com) are independent from each other and i assume dont share the same IP, downtimes from example.com dont affect sub.example.com in any way.
My answer is based on the information you provided.