|While there may be a limit on the number os client connections to a given (wifi) router... It's generally a lot more than 11.|
This is the manual for your router; page 32 is the start of wifi setup.
Is there "any" form of access control invoked (in use) for your wifi access? This can be as basic as the usual access key (and there is a default one set, and which of course one can change); and there are assorted flavours/varieties for this. There is also a system called Media Access Control (MAC) which allows three options. Allow anyone/everyone to access; allow only those in the list you create - thus disallowing access to anyone not on that list; disallow those in that list - thus allowing access to anyone not on it.
Similarly your work environment may (one would hope they do) operate/apply some form of serious access control... Preferably the latter - MAC.
So have a look-see at your home wifi setup, and see what is configured there. It may well be that if your home system uses one of the MAC options the laptop in question is not on the allow list (and previously it was) - whichever list is in use...?