Thanks for your reply, Tonny! I appreciate the help.
Yes, other devices stay connected while the laptop disconnects. I know this as I use my Android phone which is connected to the WLAN router to make Skype call while working at the laptop. Today I've seen it happen twice while I was on a Skype call: the laptop's connection was interrupted but I had no problems with the Skype call.
I also never noticed this with my private laptop and never had any complaints from my girlfriend who uses her private Android phone, her Blackberry work phone, her work laptop and her private laptop on the same router.
Unfortunately, I already did a driver update. The support page of the laptop redirects to this
page and it's pretty straightforward from there, so I'm afraid that's not it.