A little more information about your setup might be helpful. But you are saying your computer's IP address is handled correctly, but the IP address for your Gateway/Router is being changed? Is that being done by the modem or whatever you are connecting to?
Hello and welcome to the forum.
As Saltgrass has indicated a bit more information might be helpful.
What is the Model Name, Model Number, Revision Number of your network adapter?
Can you launch a command prompt on the problem PC and type
and hit enter
paste the results into your next post
In addition to not getting a proper gateway address you might also be getting just an APIPA address as a result of your adapter failing to communicate properly with your router (something like 169.254.nnn.nnn). A driver update from the adapter manufacturer's website might help this issue.
You say "Every time I restart the computer it removes my gateway address." Does this mean that you are actually setting the IP and gateway addresses manually with a static value and a reboot erases your input and reverts the setting back to automatic?
Keep us posted.
Did some more research and it seems that this is the result of a blank line in the actual values of your default gateway on that particular adapter within the registry.
You can track it down if you'd like here, but only if you are comfortable editing the windows registry as improper editing of the registry can result in serious problems overall to your computer so travel at your own risk.
All your adapters will be located under that key and the problem adapter can be located by it's IPAdress value in the right pane once you've selected it in the left pane.
Once you've identified the correct problem adapter, double click the "DefaultGateway" value in the right pane and look at the Value data: box and if there is a blank value at the top followed by correct value(s) just edit out the blank line.
If you are reluctant to do this just rebuild the TCP/IP stack and that will take care of it for you.
Follow the manual instructions listed here (since it's actually for Vista and below I'm not sure if the automatic "Fix It" will work for you but I know the manual instructions work for Windows 7)
Good luck and keep us posted.