Several PC Cannot Connect To MySQL Server on Certain Time
This has nothing to do with the MySQL server, so no troubleshooting on that side should be needed.  It is also unrelated to usernames, machine names, and passwords.   

C:\&gt;perror 10055
Win32 error code 10055: An operation on a socket could not be performed because
the system lacked sufficient buffer space or because a queue was full.


The MySQL server is not returning this error.  Windows, on the client side, is generating this error locally, when you're trying to connect, because of a resource shortage on the client system.  Of course, a reboot of the client would clear this right up... until you hit the limit again.

The most likely cause of this would be that you have an application running on those same machines is not releasing system resources properly... It wouldn't necessarily even have to be the application that's accessing MySQL but that's probably a good bet if that's the only application where you're experiencing problems.

This command, run on the client that is experiencing the problems, will list all of your currently open network sockets, as well as the name of the application that owns them:

C:\netstat -a -b -n 


Running this on a machine that is unable to connect should give you an idea of which application is causing the problem because you will likely see an inordinate amount of sockets owned by one application.

The Windows error is also known as WSAENOBUFS.