This will happen if you use textures for outlines instead of actual primitives (i.e. lines). You are fighting with twice the aliasing when you use textures to achieve this.
First the sample rate of filled primitives decreases with distance given perspective projection and second the effective sample neighborhood used for texture filtering becomes larger with distance. It can become so large, in fact, that a thin (i.e. single-texel wide) detail is completely lost despite filter interpolation.
The ideal solution would be to implement bilateral filtering for your textures (this usually gives better results than even SSAA or MSAA in this special case), but the far simpler solution is simply to use lines for the outline. Alternatively, you could use a technique I have outlined in an answer on Stack Overflow.
Now, since you're using Ogre, I have a feeling that none of the more sophisticated solutions I outlined are going to work for you. One last ditch effort would be to exaggerate the width of the border in your outline texture in lower mipmap levels (assuming Ogre gives you control over the mipmaps). Also make sure you use a
clamp to edge address/wrap mode.
I should also point out that if Ogre lets you control mipmap LOD bias, you might try a negative bias for the outline texture.