As others have said , it kind of depends on various factors. I was in a BOE once who removed an elder because one of his children stopped going to meetings even though his 3 other children were pioneers and the "child" concerned was 18. This was in the days of the book study & some of the congregation were complaining that the group shouldn't be held in the brothers house (the youngster would be watching the tv upstairs.)The vote was tight - I voted against removal & the elder gave a passionate defence of his position. Sadly he just didn't have enough support - he had been an elder for over 20 years & in that time had made a few enemies on the BOE.
Alternatively I know of an elder whose 2 children never became JWs & got into all sorts of mischief. He kept his position (as a COBOE) and his position was never threatened or even discussed. What helped him was the fact that he is quite a belligerant guy who is close to the CO & also a couple of the elders in his cong also are in a similar situation so there wasn't really any desire to delete him.
Cedars is right when he said that in many congs it is taboo to bring up the subject of deleting an elder. It is also quite risky. An elder once tabled an item on an agenda on the low field service hours of a couple of our elders in an effort to delete them but ended up almost losing his privileges himself as the 2 elders used the "attack is the best form of defence" strategy. He admitted to me afterward that he wished he had never raised it as an issue.
Incidentally Cedars - it is now the policy that if a child is going to uni / college that the elder's qualifications should automatically be considered by the BOE. I was at the meeting with the CO when it was discussed. There were a few threads about this a few years ago when this started.
To be honest , I always thought myself that if I was in that position (child not attending), I would just resign. Most sensible elders would do that - jump before they might get pushed. I went on a shepherding call once on a single sister whose child was missing meetings & not wanting to go out on the ministry. The elder I was with had 3 children , all of whom had left the truth. The sister had no respect for him & actually got quite angry. It does become something of a farce when an elder whose children are DFd or were never baptised is counselling other younger ones and / or their parents or giving talks about bringing up a family "in the truth".