My current employer said that they did not like to even offer interviews to anyone who was currently unemployed because there was probably a reason for it and they didn't want people that couldn't keep a job.
That's pretty myopic. People go through periods of unemployment for all kinds of reasons. Maybe they had a child, or wanted to travel the world. I have a computer scientist friend who took 6 months off to hike the Appalachian Trail (no, really). According to this logic, he would be a no hire. It would be the company's loss though, and I wonder if that company would be one writing blog posts about how "it's impossible to hire technical talent."
That's certainly true in tech now, when companies are scrambling to get any talent they can. But the unemployment in many other sectors of the economy is much higher, and there's not much of a competition between companies for talent.
My father used a variant of it to justify the idea of invading Iraq (a couple of years prior to us actually doing it): "Where there's smoke, there's fire."
Why should I as a hypothetical employer be particularly keen on hiring someone who has taken extended leaves of medical absence? There is a strong financial risk and no reward for doing so.
So if I ended up with a one-time sickness that put me up in the hospital for, say, 3 months, then I'm more likely to catch another long-term sickness than the rest of the general population? Logic!
In the individual case the probability can only be calculated by a physician.
In the general case? I am sure (to a certainty sufficiently high to factor into hiring decisions between otherwise equally qualified candidates) that the increase in probability it is non-zero. So yes, I am saying in the general case that people who have been seriously sick before have an elevated chance of being seriously sick again.