Hello Barbara4090,
When the iPhone unmounts from iTunes during the backup phase, it can be due to some unreadable data on the iPhone that iTunes cannot deal with. It could be data saved by a third party APP on the iPhone, but there's no easy way to determine the what data may be causing the issue.
First try resetting the iPhone by holding down the sleep/power button and home button until you see the Apple logo (ignore the "Slide to Power Off" prompt).
Connect to iTunes and Sync to test.
Next would be to determine whether the issue is actually with the iPhone or the MacBook Air.
You mentioned that you also use an iMac.
If the iMac is running at least 10.4.11 and has a current installation of iTunes 8.0.2 on it, you can use the iMac to isolate the source of the issue.
If you have essentially the same information on both computers, you can do this test in the existing user on the iMac.
If you'd prefer not to intermingle any data from the iPhone you can create a new User on the iMac and test:
http://support.apple.com/kb/HT3309
Before connecting the iPhone to the iMac, put a check in the "Disable Automatic Syncing for iPods and iPhones" in the Devices section of iTunes Preferences.
Connect the iPhone and then right-click or control-click on the iPhone under Devices and choose "Backup."
If the iPhone cannot be backed up on the second computer, then it is due to some unusable data on the iPhone that cannot be backed up.
After the test, you can delete the new User if you created one.
If that is the case, then you may need to restore the iPhone and choose the option to restore from a previous backup at the end of the restore process:
http://support.apple.com/kb/HT1414
I would do this on the computer that you normally sync the iPhone with.
If, on the other hand, the iMac can backup the iPhone successfully, then there is possibly an issue with the MacBook Air or it's software:
http://support.apple.com/kb/HT1224
Hope that helps,
Charles H.
