One of the best products that I have used to clean grout is "OxiClean". Pick it up at your nearest super market in the laundry detergent section.Use hot water and allow the powder to disolve which takes approx 20 minutes. Find the stiffest nylon brush and cover the grout completely with the solution.
I would wait about 5 minutes before using the brush. I have found if you just keep the grout wet for about an hour and some light brushing, you will be able
to get most of it up with just a clean cloth. For super deep stains, just apply more solution and scrub with the brush. Rinse with clean water and let dry. You will see an amazing transformation with new looking grout! ceramictilepro uses this product for cleaning all types of grout.
Grout that lost it's strength may be so far gone that you should cut out all the failed grout with a utility knife and get it ready for new grout. I have a great video called How to Grout which takes you through all the steps for a professional grout job that will last for years!