My family has completely severed all connection with me since I have embraced Islam and wear hijab. I have tried countless times to reestablish the connection but to no avail. Calls and messages remained unanswered untill I was blocked. When going to their home, the door was slammed in my face each time. Mails and letters remain unanswered. they do not want any contact with me at all.
Will I be held accountable as having severed these ties if I stop trying to knock on their door?

Why would you be held accountable when it is they that have severed ties with you. They will be held accountable, you've made your attempts to no avail, so as long as you are willing to connect the tie you've done your duty; they're the ones thar have severed ties.