Can Time Machine back-up files during sleep mode?

Topic.

I'm pretty sure it will not be able to do that, because most of everything during sleep mode is actually shut down.

Time machine will however backup once you wake the machine up.

It kind of defeats the purpose of sleep mode if there is something running in the background. I think Apple safely assumed that there won't be any further changes to your computer when it's in sleep mode.

If the most recent backup is that important to you then just force Time Machine to do a backup before you put it to sleep. You do this by either righting-click on the Time Machine icon in the dock or click on the time machine icon in the top right menu bar and select "back up now".

As imppy has suggested you could always wait for Time Machine to do an automatic backup when your computer wakes up.

I have about 129GB to back up, and at this rate, I won't be done until Sunday. I'm not on the computer long enough for it to finish in one sitting, and I always have to disconnect my external hard drive.

The first backup is always the longest but after that it will only do incremental backups so it will be much faster unless you routinely have lots of large files. On average it takes my Time Machine about a minute or two to backup but if you leave Time Machine on all the time then the backups should be faster because there will be less incremental stuff to backup.

For the first backup just leave your computer on and go eat dinner or leave it on overnight. This is also why getting a Firewire 800 hard drive is a nice luxury because it's faster but with Thunderbolt things should be even faster.