Static IP numbers failing

I have private static IP numbers assigned to a our clients that appeer to go bad. The first thing I have thought is how can a IP number go bad? Well that is my question. It doesnt happen often, 4 or 5 in three years. The first time it happen was with a customer that was running a cisco VOIP phone with a generic router and his computer. Every 3 days I would get a call that the computer could not get on the internet. I made a trip out, disconnected everything, hooked up my laptop, put his IP number in and no connection thru the laptop. Strange thing was that the VOIP phone worked fine but not the computer. I finaly assigned another IP number and everything started to work again, or so I thought. Three days later the same thing. Computer died VOIP works. The final solution was to put in a switch and assign 2 IP numbers. That seem to fix the problem. But Why? This week my customers on different networks seem to droping like flies. I assign new IP numbers and things seem to work just fine. Does anyone know what would kill an IP number and how do you flush that IP number to get it back in working order.
Mike