It seems like every night during our backup process, the Exchange DAG fails over. Is it possible to change a tolerance setting to prevent the DAG from unnecessarily failing over during backup times?
You have not told us nearly enough to go on, but I've got a guess. If your Exchange servers are virtual, and you're using a snapshot-based backup mechanism (like Veeam, for example), then there is a slight pause while the snapshot is taken (and/or possibly when deleted.) If you're using a VSS-capable backup process, then the backup is consistent, but the slight pause causes the other members of the DAG to think that your VM is down, so it fails over.
If none of that applies to you, then throw us a frickin' bone - what's your exchange environment, what's your backup environment? Otherwise, you're just asking us "How long is a piece of string?"