ACR wants to write the ACR adjustments into the JPG header in with the EXIF information, and it sounds like ACR cannot understand the JPG header information enough to know where it's safe to write the ACR settings.
If you turn off ACR-editing of JPGs in the Photoshop / Preferences and then open and resave each JPG at the highest quality (12). It may be that Photoshop doesn't understand enough, either, but it's worth a try. Otherwise use some other program to read and write the JPGs. You can use the Image Processor option in Bridge to batch-process the JPGs.
Hopefully the rewritten JPGs will be understandable by ACR when it needs to insert it's settings.
It might be worth backing up all the JPG files before you start the rewrite process in case something goes haywire.
You could further investigate what things are embedded in the JPG head by using ExifTool. Drag-and-drop a good and a bad JPG to the exiftool(-k).exe and compare the two screenfulls of info that show up in a scrolling DOS window.
Will try these out and let you know. Sounds entirely reasonable, so I'm hopeful, especially since Photoshop itself has no trouble with these files. (Will mark your answer correct as soon as I've tried things out.) Many thanks. GG
Haven't tried batch processing yet, but individually opening "bad" files directly into Photoshop and re-saving them as jpegs seems to solve the problem. If I ever have some time, I'll try to compare exif info on two files and let you know if I find anything of interest. Meanwhile, many thanks for your help. Saves much annoyance.