My wife's parents are likely unconverted and are living across the country from us. Most of the rest of her unconverted family is still living near her parents. Her parents are older than yours and their health is failing.
This is hard on my wife. She gets frustrated and sad. She often feels like she should be there; that maybe she could make a difference for their salvation if she were around them more. But when she does go to see them, she usually just gets more frustrated and remembers why she left in the first place.
We have to remind ourselves often that although it's good to be representatives of the gospel in their lives, we can't be taking responsibility for getting them saved or feeling guilty if we don't constantly drop everything to make one last visit in the hope that things will be different this time. As her parents age and health issues mount, the "death watch" can become a huge burden if we let it... as each visit seems more filled with both urgency and sadness.
I would suggest you not disrupt your life to try to *make* something happen with your parents. Love them as opportunities arise. Pray for them constantly. Look for chances to speak into their lives as these things come up. But don't drop everything in an attempt to force it. You can't force God's work, tempting as it is to try.
I would echo this response. My grandparents lived 1 mile from my parents house (and where I grew up), and they are (were) unconverted. My parents are both saved. My mom dropped everything all the time to attend to her parents needs to the point of spending days with them (groceries, cleaning, cooking, basically everything but bathing since they had a nurse 3 times a week).
In the end, my grandfather still wanted nothing to do with Christ, his philosophy was, "I was born Catholic, and if my religion can't take me to heaven, I don't want to go". He passed away July last year, with absolutely no evidence of salvation, and my grandmother has advanced dementia (I think it's how you spell it) so unless God's grace intervenes now, she has no chance as most the time she doesn't know her own kids.
As much as my mother (and my dad and myself) grieve that my grandfather passed in eternity without the Savior, we can't blame ourselves for not sharing the gospel. Mom and dad did it everytime they visited, only to be nearly thrown out of the house and blasphemed. When I spoke to him, tried to bring it in conversation as well, and his response was always "I know more about life than you do", to which I replied "truth is not a matter of how long you have known it, I have been saved since 2000, and the pope has been wrong all his life".
Might have not been the right response, but his decision was made. IF the opportunity presents itself (job transfer, kids, or some other situation we can't predict) that you must move, so be it. But I wouldn't move closer just to be closer. Vacations would be fine.
That's the situation my wife and I are in with her parents. Neither of us intends on moving 1400 miles closer....
Hoping this helps as far as advice goes.
Praying for you as well.