I am having the exact same problem and personaly its pissing me off. i thought it was os related as well at first because when mirc looses its connection i loose connection to my router but my router still has a connection to the internet. for kicks and grins i formated my hard drive and installed a fresh copy of windows but it didnt help.
The strange part is that the only way to fix the problem is to restart my computer. if you try to repair the network connection in the control panel it cant establish a connection. which it should be able to considering that the other computer is connecting fine.
this is why i know it's mirc related and i only have this problem with mirc. i think however it has something to do with mirc and 64bit processers. my previous cpu was an amd athlon xp and i never had this problem using the same router, cable modem, and the same version of mirc 6.16. (i haven't herd good things about 6.17 and xdcc klipper which is why i haven't upgraded) The only thing i changed with this computer was the motherboard and cpu, everthing else in my setup is the same.
heres what im working with right now: windows xp home (32-bit) w/ service pack 2 - amd athlon 64 x2 3800 - mirc 6.16