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Here's how Hidden Power works:

There are a variety of things that affect a pokémon's stats (HP, Attack, Defense, Special Attack, Special Defense, and Speed.) Some of these are obvious...some aren't. One of the ones that aren't is what are called Individual Values, or IVs. Each pokémon (not species, each individual pokémon) has six IVs, one for each stat. These IVs, which can't be viewed ingame, represent the pokémon's natural talents; aside from training and experience level, some are just plain better than others of their species at certain things. An IV ranges between 0 and 31; the higher-level the pokémon is, the more effect IVs have on its stats, and by level 100 the difference can be several dozen points.

What does this have to do with Hidden Power? The effect of Hidden Power, both type and move strength, is calculated using a formula that involves the user's IVs. A pokémon's IVs never change, so a pokémon's Hidden Power type is set from the moment you catch it. It won't change with a level-up, a Protein or Iron, evolution...it never changes. The only way to get a different Hidden Power type is to catch another pokémon.