This is the third time that I've had a leaking Presta valve on the tube. There must be a way of repairing the Presta valve rather than having to discard a good tube. Someone did it by applying glue, but I didn't watch closely enough to see where he put the glue. What can I do?
You could try rubber cement however, you will probably still have a slow leak.
You best solution is to prevent the valve from separating from the tube. To do this, I don't put the retaining nut on until after I have fully inflated the tire. Once the tire is inflated, I screw the nut on just tight enough that it won't fall off. You could add some loc-tite but I don't and haven't had a problem. If you over tighten the nut, you are going to cause the valve to separate from the tube.
Here are my two cents... By experience, rather than teflon tape I used to use a dab of anti-seize paste. Recently a presta valve broke and noticed a small rubber o-ring. Since anti-seize is not friendly to rubber over time, I switched to a dab silicon grease on the threaded shaft before it is installed.
First save the valve out of any tubes you discard (if the valve is good). And you can buy valve core separate.
The valve was two sets of thread. One to open and close the valve and the other to remove the valve core.
Removing the pump can loosen the valve core. You can use a tool such as core removal tool or a small pair of pliers to tighten the core. If it gets loose I use just a dab of locktite on the threads but you must be very careful to not get any on the gasket or the valve will stick. I have a bad set of tubes and did this to all of them up front. Just a dab on the threads in the middle. And open the valve before you tighten it.