It seems that every time I play Skyrim all the options, controls, audio and video resolution in Morrowind resets to default. Is there a way to fix this problem?

Is Morrowind installed in Program Files or Program Files (x86)? If so, move it to somewhere else. Like C:\Games\Morrowind

Easy as you can just move the install folder and make new shortcuts. Unless your using Steam, then you have do some slightly different things.