I found out something important: The problem occurs only if I suspend the laptop computers to RAM by closing the lid. However, if I click on the "K" button (KDE's "Kickoff Application Launcher"), choose "Leave" and "Sleep", wait a few seconds until I close the lid, and then resume it by opening the lid again, everything is okay and I can unlock the machine almost immediately.
I found out something important: The problem occurs only if I suspend the laptop computers to RAM by closing the lid. However, if I click on the "K" button (KDE's "Kickoff Application Launcher"), choose "Leave" and "Sleep", wait a few seconds until I close the lid, and then resume it by opening the lid again, everything is okay and I can unlock the machine almost immediately.