Many older people were immune to the Spanish Flu because they had been around long enough to have developed antibodies for a similar strain decades before.

But I've read that most common cold immunities last only for a handful of months or years, not decades.

Disclaimer: not an immunologist, no formal post secondary biological education, my thoughts on this are likely worthless.

I had the same question when it all started: how exposure to other coronaviruses affects the response to SARS-Cov-2, and what does it mean for people with different history of exposures.

One hypothesis was that older people have a higher probability of dying because their immune system does not produce antibodies fast enough to keep up with the virus. The other one was the complete opposite: that due to the long history of exposures to other coronaviruses they have too much of a response and cytokine storm as a result but that does not seem to be the case.

AFAIK it depends on how long lived the antibody response is. Memory cells can last different amounts of time for different infections, or (like for certain calicivirus infections?) hardly develop at all. Have no nice paper on hand to back this up though. But if it's a short lived response (as in years, not decades), it's good to be freshly exposed and like another commenter said, kids get colds all the time. And likely parents of young children too (I know I did). Maybe that helps?

Coronaviruses aren't that common to the point that people are repeatedly infected with then throughout their lifetime.

The immune system in the elderly also deteriorates with age, so it's not as effective.

Yes, but they could have other risks due to existing medical conditions. It's an arms race between the speed of replication of the invading virus, and the immune system's ability to respond. Existing conditions add many complications.

If they interact regularly with family and were long exposed to commonly circulating viruses (e.g. from kids), they would have a resilient/diverse immune system. This assumes a healthy diet with no deficiencies (Vitamin C, D, Zinc).

Another complicating factor is the content of flu vaccines.