Linked images – links get broken

Where are the original graphics files from the previous issue stored on your system/network/cloud storage environment? Does the same result occur when you put those old images into the new document using the File>Place... menu command? 

If that works, you may find that using the File>Place... workflow is faster than your current copy-paste-relink solution. This is the preferred way to put graphics in any InDesign document.

Randy

After you have moved the images to a new folder, you could select all the missing link images in the Links panel and choose the 'Relink to Folder…' from the flyout menu of the Links panel to relink them all in one go.

Are you sure InDesign loses the path? Since you say "thes months folder" it sounds like you are moving the files. If you have images that are to be reused they maybe should be in another stationary folder that is for permanent images.

The issue coould also be with cloud storage, and that is more hard to explain. iCloud, oneDrive and other file management systems will sometimes make it look like you have files on your drive but they are only available "on demand" There is usually a small cloud icon on the icon to show that the file is not actually on the computer. If this is the case InDesign cannot find the file because only its ghost/alias is there. This is obfuscated by operating systems. You would have to tell the operating system /cloud service that you want that folder permanently on the computer (which you may not want if you have a monthly folder)

If it is just one or two brand elements that you want to permanently add to an indesign file there is also the option to embed the link. Note that if the link is edited the embedded link is another independent instance that will not automatically be updated. Embedded images will also make the file size bloat, and it is not optimal where you want to deligate image processing or optimisation. (Even if office applications would normally embed rather than link) 

It is hard to give this a quick fix but one would have to look at your whole workflow and how you would want to organise your files for best efficiency.