Keep backing up when I put machine to sleep? I use Time Machine, with an external hard drive connected by USB, to back up my MBA.  If Time Machine is in the middle of backing up my drive and I close the lid of my computer, Time Machine will stop the backup and (as far as I can tell) will not resume backing up until I wake my computer back up.

Is there a way to change this behavior?  I want it to continue backing up, until it finishes the backup, even when I close the lid of my computer in the middle of a backup.  Is there a way to do that?
Your observation of how Time Machine is backing up is the same as mine. If TM is running a backup and you put your machine to sleep it will resume that backup on wake, but it will not keep your Air awake when you close the lid Unless you wish to prevent your Air from going to sleep when you close the lid, this is the expected behavior.

Time Machine takes its sweet time, especially if you have a chunk of data that needs to be backed up. I tend to let my backup finish by plugging in my machine and running Caffeine and then putting it to sleep later. The truth is, though, I've never had a real problem with the backup restarting on wake.