I don't see where you're located (every State has different legislation) but in my market, all three of the criteria you mentioned would be unlawful reasons to decline an application.

As the foreclosures decline it would be even more challenging. 

My understanding from Jamie (this is not legal advice) is that while your property may not qualify for Section 8, you still are not allowed to decline tenants because they are using a section 8 voucher.  

A lot of Tryon road is where things start to decline in quality.

I'm curious about your thoughts/recommendations here...I have a 2 bedroom unit with two tenants with declining health. 

Analyze whether you can stomach a 20% decline because the prices can decline in the short term.  

I declined as I'm not going to commit to paying an unknown amount. 

The average price declined 2.1 percent to $270,303.The HAR sales report indicated a decrease in upper-end sales.Check out the the Center's fourth quarter 2017 housing report for Houston-The Woodlands-Sugar Land for more data. 

And there’s no tax benefit to doing so, it just declines in value everyday, there’s no “cash-flow” to think of, but the kids don’t want to cajole dad into selling his car.

If you try to get a HELOC from a mortgage broker the rate will be crap (if they can do it at all), if you try to get a purchase investment property loan from a credit union or big bank then it'll take 4 months just to be declined at the last minute because your CPA didn't dot an i on page 7 of your tax returns, etc etc, you get the idea.