What can make a radish lose its flavour in a dish?
I don't think anything reacted, just that you smothered them in other stuff. 

Some of your additional ingredients (the cream cheese and the miracle whip) will soak up any taste present and dilute it. If you just made cream cheese with radishes, it will still taste a bit like a radish, but much weaker. 

But you didn't just dilute it, you combined it with other, very strong tasting food. Mustard, pickle and liquid "seasoning" are all little taste "bombs" which will easily overpower lots of other stuff (and tuna isn't so weak either). Especially the mustard has a taste and aroma which is very similar to radish, but much stronger - it will probably mask the radish. The actual radish taste (beyond the hotness) is very delicate and easily covered up. The hotness itself is the same as mustard hotness, only weaker, so it disappears into the mustard taste. 

With this mix of concentrated tastes and dilutants, it's no wonder if your radish taste just went under. 

If you want your salad to taste of radishes, you should remove most of the stronger seasonings. Or just replace the miracle whip with radish paste. 

I doubt that adding an acid or a base will have much effect, or that you'll be adding any bases at all. Basic food doesn't taste too good, especially in combination with fat.