Scan never completes

The log shows you gave it several hours (good test), that it is a 'Scan This Mac' scan and that the scan detected (and is scanning) the main hard drive and the backup drive all in one go.

If it was me I wouldn't bother with scanning the backup volume.  Why is it really needed?  Let's say that there may be malicious files in backup...they aren't going to cause any problems being in there - they are locked up in the backup.  The backup with them in will eventually be deleted when Time Machine fills up the drive and needs the space.  You may decide to pull files out of the backup and one or more may be malware.  However the real time scanner will immediately detect them at that point.  My advice: exclude the backups and just scan the main system drive because that's the important bit.

If you agree it's not required then you can either create a custom scan (which you can schedule to run whenever you like - the computer has to be on though).  In the scan include the main drive, but exclude the 'Backups' volume.

Main drive scan:

Include items: /

Exclude items: /Volumes/Backups

Or you can re-configure the 'Scan This Mac' scan in the same way - to exclude the /Volumes/Backups folder - and whenever you run it, it's just going to check the main drive.  To re-configure this scan just double-click the white area in the 'Scans' window and access the 'Scan This Mac' settings.

Optional: If you really wanted to set up a scan for backups volume then you should create a standalone custom scan where the 'Scan Items' tab has just the /Volumes/Backups listed.

In summary:  I suggest you either configure 'Scan This Mac' to exclude the backups volume or create a custom scan with the same exclusion  - your choice.  Then see how long that scan takes.

If the scan still takes a really long time (give it time on the first run) you need to identify if it's a particular file etc. that is causing a particularly slow scan time with the Sophos sweep program from Terminal to log the files being checked.  Example:

sudo sweep / -dn 2> ~/Desktop/manualscan.txt

Hope that helps.

The log shows you gave it several hours (good test), that it is a 'Scan This Mac' scan and that the scan detected (and is scanning) the main hard drive and the backup drive all in one go.

If it was me I wouldn't bother with scanning the backup volume.  Why is it really needed?  Let's say that there may be malicious files in backup...they aren't going to cause any problems being in there - they are locked up in the backup.  The backup with them in will eventually be deleted when Time Machine fills up the drive and needs the space.  You may decide to pull files out of the backup and one or more may be malware.  However the real time scanner will immediately detect them at that point.  My advice: exclude the backups and just scan the main system drive because that's the important bit.

If you agree it's not required then you can either create a custom scan (which you can schedule to run whenever you like - the computer has to be on though).  In the scan include the main drive, but exclude the 'Backups' volume.

Main drive scan:

Include items: /

Exclude items: /Volumes/Backups

Or you can re-configure the 'Scan This Mac' scan in the same way - to exclude the /Volumes/Backups folder - and whenever you run it, it's just going to check the main drive.  To re-configure this scan just double-click the white area in the 'Scans' window and access the 'Scan This Mac' settings.

Optional: If you really wanted to set up a scan for backups volume then you should create a standalone custom scan where the 'Scan Items' tab has just the /Volumes/Backups listed.

In summary:  I suggest you either configure 'Scan This Mac' to exclude the backups volume or create a custom scan with the same exclusion  - your choice.  Then see how long that scan takes.

If the scan still takes a really long time (give it time on the first run) you need to identify if it's a particular file etc. that is causing a particularly slow scan time with the Sophos sweep program from Terminal to log the files being checked.  Example:

sudo sweep / -dn 2> ~/Desktop/manualscan.txt

Hope that helps.