I'm running ERA 6.2 and I have noticed the same behavior for many of my computers. There is a dynamic task in the "client tasks" which will run an "in-depth with cleaning" scan on any computer that is placed in the group "computers with active threats". My Surface Pro 2 was the first and only ESET 6 Agent enabled computer while testing and I noticed that my laptop was running something idiotic like 5 scans a the same time.
I'm very mobile as well so when I move from my docking station to wireless and then back, I noticed another scan started up. This is after it had finished the 5 previous scans... then a few more scans would start.
I thought my laptop was also starting scans when unlocking so I tried turning down the "startup scan" settings (since you cannot turn OFF the startup scan).
The dynamic scan for the group "computers with active threats" when computers are added to the group has some kind of flaw in ERA. If the computer does not clear the threats, then it starts another scan, then another, then another.
I have a few machines that had 24 separate scans run in the course of 1 day. All because of the something like ASK TOOLBAR.
They are not fast scans either of course and take up to 1hr each because they are "in-depth"
Deleting this dynamic task will stop the multi-scanning... sort of. There is still times when I notice my laptop running 2 scans at the same time and I think it has to do with the startup scan or somehow thinking that my changing network connections is causing a scan to start. So now I have to check ERA every couple of days and run a manual "in-depth" scan on every computer in the list which has something benign like ASK which gets pushed alongside of Java updates.
It's just ridiculous though. I can't figure out where all these scans are coming from.