We have a pink marble tile that has some brown veins and the veins are soft and coming out. Is there anything we can do to stop these veins from softening?

The material you are describing is probably a marble known as rossa perlinio. This type of marble, when it is formed has mud running through it and this is what the soft veins are---mud. Unfortunately the only cure is to fill the veins as the erode out.

TIP These veins can be filled with polyester or if you have a lot of veining you can use a colored unsanded grout.