Are homemade versions of popular food more liable to spoil?
Its less that the simple act of cooking it at home causes shorter life of the product and more that at-home cooks are cooking for the sake of avoiding the chemicals and preservatives that are what give the commercially made things their long shelf life. 

In some cases it is preservatives (sulfates in dried fruit (I think)), in some cases it is an extra processing step (ultra-high-temp-pasteurization for organic milk), while in other cases it is a matter of equipment that is simply not available for the home cook (for example canned pureed pumpkin - this is not safe to make at home (even with a proper pressure canner) but with the commercial equipment and processes it becomes shelf stable). Usually I think it is a combination of all three of these.

That being said, in regards to ice cream - I recently read somewhere that if you put the container with the ice cream in it into a Ziplock baggie then it helps it stay soft for longer.

I still have some ice cream (technically sorbet) in my freezer from over a year ago that I keep forgetting about. When I decide to chip some off the solid block it has become (I did not store it in a Ziplock baggie, just a container) it is still quite good.