Aargh! This is the third time my bra’s underwire has pierced through the fabric of my bra. I thought I had repaired the problem by pushing the steel underwire back in the bra, and hand-sewing the hole shut. But apparently, the underwire is sharp and keeps cutting through.
Anybody know how to repair this more lastingly ?
I feel your pain, Maastricht …literally! That happens to my bras too. And mine are very expensive . Usually around $40 a bra. 
I have found that there is usually a little plactic tip on the underwire that breaks apart and falls off, leaving the sharp end of the wire to poke its way through your bra.
I have had some success shoving the thing back in the hole and squirting a tiny bit of hot glue (with the glue gun) in there before hand sewing the hole shut again. If the hole is really bad, I have even sewn a small piece of felt over it for extra reenforcement.
I’ve had some success with using the heavy cloth adhesive tape that used to be sold for first aid (I haven’t seen any for a while, come to think of it.) I’d tear a small piece off and use that to replace the plastic tip thingy off the underwire, then sew the hole up by hand. Good old duct tape might be pressed into service here, too.
I chop the thing off an inch or two with some wire cutters.
I’ve done all of the above. Duct tape works the best. Seriously. The good news is now it comes in colors! 
I used to have this happen all the time, and in my experience, no matter how you try to sew it up, it will come back out and stab you in the armpit. I read that this is caused by drying them in the dryer, which melts the plastic doohickey that covers the end of the underwire. Washing bras by hand is a major PITA, so I wash them in the washing machine, then pin them up by the metal eyes on a bulletin board to dry. I also scour the clearance racks at Target and such for bras and underwear when I have a little extra cash. Sometimes you can find things amazingly cheap, if you don’t mind some odd colors and prints. I picked up some nice underwire bras last month for $3, and I’ve gotten some comfy (although orange/pink and aqua/brown) bikini panties for $2 for 2. But hey, they are cheap, comfy, not gramma looking, and cover the bits what need covered.
I don’t know nearly as much about bras as I’d like, but would it be possible to file the end of the wire into a more rounded (i.e., less sharp) shape? One might even do this in conjunction with the other offered methods, to make the duct tape or whatever last longer before the wire pokes through it.