There could be any number of reasons for this type of issue. WINS / NetBIOS, DNS, etc.,
Save yourself some hassle.
Give your server a static IP address, suitable to your existing IP schema and outside the scope of any DHCP server present on the network (exclude it if necessary or restrict the scope to exclude it).
Map all your network drives using \\IpAddress\ShareName like.......
\\192.168.1.10\Docs (where 192.168.1.10 is the static IP address of the Server and Docs is the resource on that server you wish to map on your client machine.