My first shader with alpha, disappears at distance

Hello there. I'm starting to take a look at shaders; Predictably, perhaps, things are not going as smoothly as they could. I've spent another day reading blogs, answers and the Unity Manual and I've finally started editing my first shader, based on the 'Rim Lighting' shader on this page.. http://docs.unity3d.com/Manual/SL-SurfaceShaderExamples.html

Here's my edited shader:

 Shader "Unlit/sun shader"
 {
     Properties {
       _MainTex ("Texture", 2D) = "white" {}
       _RimColor ("Rim Color", Color) = (1, 1, 1 ,1)
       _RimPower ("Rim Power", Range(0.5,8.0)) = 3.0
       _Color ("Color", Color) = (1,1,1,1)
     }
     SubShader {
       Tags { "RenderType" = "Opaque" }
       CGPROGRAM
       #pragma surface surf Lambert alpha:fade
       struct Input {
         float2 uv_MainTex;
         float3 viewDir;
       };
       sampler2D _MainTex;
       float4 _RimColor;
       float _RimPower;
       float4 _Color;
       void surf (Input IN, inout SurfaceOutput o) {
           half rim = saturate(dot (normalize(IN.viewDir), o.Normal));
           rim = (rim * rim) * 2;
         o.Albedo = _Color.rgb;
         o.Alpha = rim;
         o.Emission = 1;
       }
       ENDCG
     } 
     Fallback "Diffuse"
   }

Instead of adding Emission lighting at the edges, I'm reducing the alpha so that the spherical object appears to glow and fade at the edges. This is mostly working fine, with one annoying problem: The object is now only displayed as I get very close to it. Can anyone tell me why this might be? When I use a standard shader the object is drawn at the distances I expect so it's not a far clipping plane problem.

Is there anything in the shader that's causing it to appear only when very near? Any help, much appreciated!