What files are they (e.g. what kind of archives)? Are they some big archives (being unpacked by avast! to TEMP dir to scan its content)? Do you have enough free space on the drive where the TEMP dir is located?
What OS are you using?

Btw, if you want to check for sure what file it got stuck on, you can go to Settings and tell avast! to create the report file (with OK files reported as well).
What happens when you copy the file is usually gets stuck on to an empty folder and scan just that folder?