I've been setting up networks since before ethernet was invented, and I don't recall ever having to worry about DHCP lease times causing loss of connections.
As these new OS's come out, they use ever more complex security protocols. sometimes the router will not hook up properly to the ones with the new OS.
The fix is to raise the security level to WPA from WEP on the entire network, assuming the router will allow it. This sometime require the purchase of a new router, or the reconfig of the default options on the new computer to WEP from the default WPA. It is lees effective security, but you need to do one or the other.