Esse, I will relate to you my personal experience with a situation similar to the one you describe. However, because it is my own experience, it may be somewhat outdated. And I apologize for the length - I can be a bit long winded.
This event happened in 1971, a couple years after Franz had made his !969 summer assembly announcement about 1974 marking the 'end of the Gentile times' - I attended the Vancouver Assembly in 69 when I was 12 years old - and so began the ugly times. My mother was disfellowshipped the following year for 'unChristanlike behaviour'. And my father, a Ministerial Servant, who had attended Toronto's Kingdom Ministry School, became inactive and my parents were sort of separated.
I was forced, by both my parents, to continue attending meetings and going out in field service with my older brother, who was being groomed for elder status, and my older sister. This continued for about a year. I was never baptized. And I hated it the whole time. I absolutely despised everything about the Kingdom Hall and the religion.
At the age of 13, I got my chance and put in my heels ( a long story that involves a go-cart and a broken ankle) and refused to go back to meetings. About two months into my rebellion, I received a visit from the two top guys in the congregation. They had to have watched the house and timed their visit when they knew I was home alone. My mother worked. Keep in mind, I was only 13 - a young minor girl.
They came in the house, sat down and promptly asked me why I wasn't at meetings, read some Bible scriptures to me, and asked me "if I wasn't worried about Armageddon coming Real Soon?".
I was very scared, but also pretty angry by this time, but the anger helped me get over my fear and this is what I said to them:
"Well, correct me if I am wrong, but, what you teach at the Kingdom Hall about Armageddon is that, when it comes, all the babies and children of the people who are bad and turned away from Jehovah will be judged on their parent's actions, right?"
Of course they nodded, pleased that i had learned my lessons so well. And then I said:
"Well then, I don't see the point of me attending meetings, because, if Armageddon could come tomorrow like you say, then I won't be saved anyways, so it would be a waste of time for me to go back to the Kingdom Hall. Because my Dad doesn't go to meetings anymore and you guys kicked out my Mom for working in the bar. And I am not baptized. So you will have to leave and don't bother coming back."
And that is almost word for word what I said. Even though it was so many years ago (my gawd - way too long ago!), it was pretty much the most important moment in my life so I remember it really well.
I showed them the door and told them not to bother coming back - I was scared and shaking. I phoned my Mom at work. She phoned them and tore a strip off them both for coming in the house when she wasn't home. She was pissed.
Over the years, I have been targeted off and on by local JWs who know me. However, during the past few years, most of those back in my home country give me wide berth when they see me. We have had several encounters that have not ended well and I am well known as an outspoken critic of the Watchtower Society. In spite of that, there are a few JWs that I have a nod and smile relationship with.
My mother has remained disfellowshipped for the past 45 years but she is still on the call list for visits from the local congregation. She is in her 80s and will get the obligatory visit from a local elder and the CO when he is in town. They read her a scripture or two and ask her if she wants to come back to the fold. She says no and they leave. And return the next time the CO comes to town.
And by the way, she was one of the JW children baptized right at the beginning of WW2. The Canadian WTS sent men around to rural Canada to do a sweep of baptisms, especially children, and she was baptized at 6 years of age, in 1939. And then disfellowshipped years later, when she was in her 30s.
So, in answer to your query about if 'They' ever give up, I can only answer from my own experience and, unfortunately - no.
Orphan Crow