Because the comments seem to have constituted a satisfactory answer, I am copying them here for the record (and adding a few edits to improve them).
How could the values not change? Consider what happens during the reprojection. Because the raster is truly being warped, each cell in the new version has to reflect some combination of values from the original raster. Except for some special cases there cannot possibly be a perfect match of values between the rasters.
(The "special cases" are where the amount of relative warping is so small that there is a one-to-one match between input and output cells and you specifically request that no interpolation be done--that is, you use "nearest-neighbor" interpolation.)
Perhaps what you should ask instead is "what can I do to control how the z-values are interpolated during the reprojection?"
So it's normal that the highest/lowest value changes about 10 meters? That's odd :/
That's not in the least unusual:. The default interpolation by most systems uses some kind of (weighted) average, such as "bilinear interpololation." Averaging, by its very nature, decreases large values and increases small ones. I have seen z-values for mountaintops decrease by over 100 meters upon reprojection. (This happened in a 1Km resolution DEM of Haiti, for instance.)
Understanding this phenomenon will help guide you towards effective strategies for maintaining raster data; in particular, it should now be obvious that you want to minimize the number of reprojection procedures when going from raw data to the final data that are mapped or analyzed.