Internet disconnects repeatedly

I have a network which consists of a Netgear FVS318 router, linksys 16 port switch,linksys wireless router and a dsl modem. I have 9 computers connected thru the network, (2) being wireless laptops. My problem is the computers keep losing internet connections. (DSL thru Bellsouth). If I disable and enable the local connection on any computer internet access is back on line, sometimes this works the first time and other times it takes two or three attempts. I’ve contacted Netgear and uploaded software to the router but I still have the same problem.
I ready need some help on this one.

Thanks in advance,

netstalker