This is typically the case when shooting something that is white on white, like the embroidered USA I just finished. Natural light will reflect off the white on white subject leaving the lighting uneven and can compromise the details in your picture.
Have no worries, there is a solution and the solution is simple. Add additional light. Invest in some clamp lights.
Clamp lights which are sold at most home improvement stores for about $5 or $6 dollars a piece. 2 should be enough to provide additional lighting on each side of your subject.
To build upon previous 'Go Manual' photography tips, set your camera to 'tungsten light' to push the quality of your pictures even further.
So, next time the sun isn't cooperating with you, get out your clamp lights and make your own light.