Unable to obtain DHCP lease renewal

One of my remote lans issues IP addresses via DHCP. Periodically, one or more of the PCs will lose network connection because their leases have expired. How long after you issue a ipconfig/renew should a new lease be acquired … better yet, how can I prevent leases from expiring? This does not seem to be a problem on 2 other lans with DHCP servers. If I do nothing for a day or two, the problem resolves itself but in the meanwhile the users do not have access to some of the shared network resources (ie printers).
As a secondary question, how long after you add a new PC to the LAN(consists of about 30-40 PCs) should you typically expect to see it on the network neighborhood?