InDesign should be able to open documents from earlier versions of InDesign without any problems. Just open the previous issue and edit the file. You could open the most recent file and create a template from that file so that any future issues you can just open the template and edit the template without having to worry about importing older formats.
Frankly, "recycling" files like this is a recipe for disaster down the road when you least need it.
Create template files and use those so each issue is a new clean file made from the template, not a recycled previous issue.
Peter gave you an excellent answer that you should consider for putting together new issues of your magazine. Please take the answer he offered to heart. It'll make your life a lot easier in the long run.
But if you need to grab elements in those archive files, you will still likely need to reach in those old issue document files. InDesign, for the most part, does let you open document files from older versions of the program in later versions. But there can be some issues. If you could please share some more information, we can give you a better answer to your question:
1) What version(s) of InDesign were used to create the old issues?
2) What version(s) of InDesign will you use to create the new ones?
3) What computer(s) were used to create the old issues and what one(s) will you use to create new issues? Because if the old files were created on the Mac version of InDesign and the new issues will be produced on Windows PCs, that will introduce new issues.
Getting that information from you will help us get a better answer to your question. Thanks.
I was a bit abrupt last night and should have added more information.
I stand by what I said -- make templates. I should have added that we see one or two posts every year from someone who does a periodical of some sort whose document has developed a permanent fatal and non-recoverable problem and the workflow inevitably involves recycling. This is even more likely if there have been version changes. We see similar fatal problems with many files that are directly converted from a legacy version to the latest version, with the probability of trouble increasing as the generation gap expands or the document is converted through multiple generations.
This does not mean you cannot copy content from an older file. In my experience that is generally safe, but in most cases no more efficient that rebuilding.