The place to configure your DNS servers is /etc/resolv.conf. It will contain something like:
Nameservers are specified using the nameserver option and are used in the order they're specified, so this client will use 192.168.0.1 unless it doesn't respond for 5 seconds, in which case it will try 192.168.0.2. The search option is a list of domains suffixes to add to requests if a lookup fails (By default if your query has no dot in, and therefore probably just a hostname, the resolver will not do an initial query and just try adding the suffixes).
This file is normally static. You would normally edit it by hand or use some GUI tool to do it for you. This is what you are doing when you use the networks connection settings.
However, if you have an interface configured for DHCP, the DHCP server can give out nameservers, so the DHCP client has to update the file. DHCP requests will normally happen at boot time and also when the lease runs out (which is controlled by the server; could be hourly, daily or anywhere in between).
It is also possible that some other configuration system is rewriting your resolv.conf on boot up. Linuxconf was prone to do this. You might find a comment in /etc/resolv.conf warning you not to edit the file because it will get overwritten if this is the case. This might give you a clue what to change.
As you have to keep reconfiguring your servers after boot and you don't specify what version of linux you are using, I'll make an assumption that it is DHCP causing the problem. There are a couple of solutions. First, you could change the DHCP server to give out the right DNS servers. This may not be desirable or possible if you don't control the server or you don't want everyone on the network to get those DNS servers. The second solution is to tell the client to ignore the options from the server. You may find a GUI option to do this, but more likely, You're going to have to do this by hand. You can do this by editing dhclient.conf (/etc/dhcp3/dhclient.conf on Debian and Ubuntu) and adding the following line:
supersede domain-name-servers 192.168.0.1 192.168.0.2;