There may be several explanations for this behaviour, but the most immediately obvious one is the backup file has been corrupted, that is the xml file has possibly been damaged in some way. In the v2.7.2+ create a backup file. Download it, chence the file extension from mbz to zip, unzip it. Do the same to the v2.7.1 backup file and look at the xml file of both backups. is there any weirdness in either one? Look at the file structure of both backups, are they similar, or very different? They should be similar, if not the same despite being different courses. If the xml file has been damaged, it may not be unzipping the file properly, hence the spinning wheel.
Another possibility is that the downloaded v2.7.1 file has been damaged during the download process, (which has been known to happen but not to my knowledge for a long time), or the installation was not quite as smooth as possible, and something was not properly copied, or installed during the install process. Downloading the latest version and replacing the standalone usually fixes anything resembling that. Another way to fix these things might be to replace just the file handling/upload/d'n'd and backup/restore sub-folders in the Moodle code.
Sorry about the shotgun approach here, but these things all fix different problems, and from the information given, it is not really easy to determine what the actual problem is. Try one thing, then the next, then the third and so on. Good luck.