Unable to back up iphone to the computer

Question

There are two iPhone 5c's in my home.  I am able to back up one to my computer with no issue.  I get an error with the other (16GB, running iOS8) that I am unable to back up the iPhone to the computer.  I have tried this iPhone on THREE computers and get the same error each time.  One of computers never had iTunes installed on it before and I was still unsuccessful.  Following the instructions provided on this site for this issue has not helped and resetting the lockdown folder only prevents iTunes from connecting to the iPhone at all.
I have noticed this error in the log file:
[com.apple.console AppleMobileBackup.exe] Unable to move temporary file "C:\Users\[user]\AppData\Roaming\Apple Computer\MobileSync\Backup\Logs\MobileBackup-unknown-20140918-212429-Backup-Com puter.log" (3)
[com.apple.console AppleMobileBackup.exe] Unable to move temporary file "C:\Users\[user]\AppData\Roaming\Apple Computer\MobileSync\Backup\Logs\MobileBackup-05351e3d71b2ce92eea74258a6d3361009 a32275-20140918-212429-Backup-Computer.log" (3)
[com.apple.console AppleMobileBackup.exe] WARNING: Backing up 05351e3d71b2ce92eea74258a6d3361009a32275
[com.apple.console AppleMobileBackup.exe] ERROR: Backup message response: 104 Multiple errors uploading files (MBErrorDomain/104)
This folder doesn't exist.  The path exists down to Backup, but there is no Logs folder.  Creating the Logs folder to the create the hierarchy does nothing.
When I delete the 05351e3d71b2ce92eea74258a6d3361009a32275 folder which actually does contain files and try to back up the phone, iTunes will actually recreate that folder and begin writing files to it.  It seems to get partway through the backup process and then report the error that it cannot back up the phone.  Something corrupt on the phone?  I've deleted all, but four photos on the phone.  I believe I read in one thread that some people were having success by deleting photos.  Unfortunately, I did not.
Since this is happening on all three computers, I would have to say that something is up with the phone.  Normally I would throw in the towel and wipe the phone and start over, but my wife just lost her mom and there are text messages on this phone from her mom.  I have to be able to back up this phone so when she gets a new phone she can take those texts with her.  Someone out there must have an answer for this.
Thanks.

Answer 1

Coleman,
I had a similar issue.  I was neither able to back up to iCloud nor to my computer through iTunes.  When I tried to do so to my laptop, iTunes would display the following message:  "iTunes could not back up the iPhone [myiPhone] because the back up could not be saved on this computer."  I looked at the system log and saw the same error as you.  When I tried to do so to iCloud, my phone would display the following message:  "The last backup could not be completed."
On my laptop, I did the measures suggested by this article:
http://support.apple.com/kb/TS2529?viewlocale=en_US&locale=en_US
None of that worked.
On my iPhone, I tried the following:
Turning off backing up for the camera roll.
Deleting the backup for the iPhone in iCloud.
None of that worked.
I did not want to do a factory restore, so I decided to contact Apple Support.  My case got escalated to a senior advisor.  He suggested that I turn iCloud backup off (Settings > iCloud > Backup > iCloud Backup) and reset all settings on my iPhone (Settings > General > Reset > Reset All Settings).  Once that was done, I reset my phone (press and hold both the Sleep/Wake and Home buttons for at least 10 seconds, until you see the Apple logo) and reenabled iCloud backup.  I was finally able to back up both to iCloud and my computer.  Fortunately, all of my content, including messages, was preserved.
I hope this helps.
-Dante
MacBookPro10,1:  OS X 10.9.5 (13F34)
iPhone 5S:  iOS 8.0.2 (12A405)