Deteriorating tub tile grout can be repaired

Q. I’ve got a partially sunken tub and shower that’s got a mixture of different tiles. The tub is cast-in-place concrete and was hot-mopped with asphalt to prevent water leaks. The grout between the mosaic tiles is eroding slowly, but the wall tile grout is in very good condition. Is mold causing the tile grout to erode? Will the eroding grout cause leaks? Should I just demolish the tub and shower and start over, or is it possible to repair the grout? How do I stop the mold from grow