In theory, a digital file can be preserved forever just by recopying it before it degrades beyond the point when you can read it. Straight bit-for-bit copies can be made as many times as needed with no loss of data at all.
The (potential) problems are the file format and the storage medium.
Make sure the file format you use doesn’t use any “lossy” compression. JPGs (or JPEGs) are almost always a compressed file format that discards some information that is usually not missed, or not missed much. This gives very good compression on many images, so the storage sizes are smaller. Save a file using a lossy compression format like JPG more than once or twice, and it becomes VERY obvious. Even a single save loses some information, and sometimes a lot of information. These formats should always be avoided for any kind of storage where you want to preserve an image.
Other formats, such as TIF (TIFF), PSD, GIF, etc., are usually not lossy, and should be used for storage.
The second problem with file formats is also the problem with storage devices. Will you be able to read them at a later date?
As fast as the computer industry changes, file formats and storage devices come and go at an alarming rate. I’ve got backup tapes made only 6 or 7 years ago that I can’t restore because the tape drives aren’t made anymore. Optical disks that were widely used 8 or 10 years ago are now just coasters for the same reason. I’ve got gigs of data on Zip disks. Who knows if Zip Drives will still be around 10 years from now? The CD has been around for 20 years or so, but will CD readers still be available in another 20 years?
The same thing can happen with file formats. Use a format that is proprietary to a particular program and you are (more or less) dependant on that program to retrieve it. If that program isn’t available, you’ve probably lost access to that file. I have backup files made on diskette (which are rapidly going away, it seems) that were made with a backup program that no longer exists. That data is essentially gone.
So high quality digital copies can be a great way to preserve data. But make sure that you copy them every now and then to a new storage medium, and use a current loss less file format. In that way, you should be able to keep them more or less forever.