Even if your grout was installed properly to begin with, it was never meant to last forever. Years of exposure to a moist environment and cleaning with harsh chemicals will make your grout crack and fall out. Around the base of your shower, or in the space where your tub meets the tiled wall, moisture collects until it eventually runs off. Over years, grout in these areas may become stained with mildew. Cleaning these areas with bleach or other mildew-killing products can cause your grout to wear away more quickly than in other areas.
If this area of your shower was recently regrouted, then the new grout may not have been properly installed. Old grout must be removed before new grout can be installed. To remove old grout, you must use a carbide-tipped grout saw. If this step was skipped when you regrouted, then the new grout is falling out because it is not properly adhering to the old grout. To fix this problem, you must remove the new grout, any old grout and then you must grout again. If you removed the old grout before installing the new, you may have mixed your grout improperly, or you may have used the incorrect type of grout. Nonsanded grout is only appropriate for tile joints 1/8 inch or smaller. For larger joints, you must use sanded grout. Follow the manufacturer's instructions when mixing your grout, or consult with a tiling professional.
If the grout is falling away from the seam where the shower meets the wall, then this may be happening because the shower and the wall are moving independently of each other, creating a crack between the two. You can fix this problem by regrouting, but you will likely be faced with the same problem down the road. You may also remove the grout and replace this area of your shower with caulk. Caulk is flexible and somewhat stretchy and will not crack with the natural movement of two independent bodies in your bathroom. Unfortunately, caulk only lasts a couple years. It is more susceptible to staining from mildew. When it starts to look very bad, you will want to dig out your old caulk and replace it with new.
If your new grout is only coming out near the base of the shower, and nowhere else, this could be an indication of moisture problems behind your shower base. Moisture damage sustained over many years can cause thousands of dollars in damage. If you suspect this could be your problem, consult with professional to find out if there is a leak behind your shower.
To increase the life of your grout, never use harsh chemicals such as bleach to clean your grout. Sealing your grout prevents it from staining, making it easier to clean without bleach. Clean your grout frequently with natural bathroom cleaners and soft brushes or sponges.