It seems the timeout for dialog to disappear is 15 minutes. After the 4th scan I finally got the information I needed. Strangely, during the rescans it counted the threats known from the previous scans, but it didn't show the threat dialog for them after the scan. With disabled automatic healing it didn't put the files to quarantine and it seems there was no way for me to get the file paths/names of the suspicious files. I had to reboot the machine, restart the scan and monitor the scan progress and be fast enough to hit the 15 minutes interval when the scan finishes. Then I got the data.
It seem the live grid works, because after the 4th scan the report from heuristic for suspicious files was much shorter than from the 1st scan and there was finally only one threat reported which also looks like false positive.
Overally, it seems good, but this auto-closing feature is really strange.