ricecrispies

One of my Schrader valves appears failed suddenly as I was pumping the tyre. The tyre went flat in a few seconds. I tried unscrewing and reattaching the pump, but the tyre still won't pump up.

Can I be sure that the problem is the valve and not the connector to the pump?

If it is the valve that is wrong, can I fix it, or do I need to replace the inner tube?

CliffordK

If your pump is OK, it should be able to pump the other tire.

Valve cores are replaceable, but would rarely suddenly fail catastrophically.

I'd remove the tube and inspect the tube to see if you can find where the flat is. Note where the tire is mounted in relation to the valve in case the problem is away from the valve.

When inflating the valve should be 100% straight. An angled valve can cut the rubber around the valve and cause failure.

Burrs in the metal?

On rare occasions valves will pull away from the tube.

Tamiya

It's called a puncture, yes replacing inner tube is surefire repair... best workout what caused it & remove that cause.

When the pump is attached to the schrader valve, the valve core is opened & plays no part in keeping air in. You can even pump up the tube with a valve core, it just won't hold air after detaching pump.

ricecrispies

Ha ha ha! Clearly the world isn't ready for my level of genius! I feel a bit embarrassed now...

Unca_Sam

It's early, don't be embarrassed.

I've had this happen because of old rim tape. First! pay attention to how your tire is positioned in relation to the valve stem, you'll use that as a map to locate the offending area of your wheel. Dismount the tire and inspect tube for leaks. If it's on the inside circumference, you'll want to replace your rim tape because it's not keeping the tube from pushing through the spoke holes.
I've assumed you have double wall wheels. Either way, you'll be able to find the leak to patch and look at the wheel or tire to see what damaged the tube.

Litespeedlouie

Possibly the valve core has just loosened and can be retightened with a valve core tool. To this day, I make sure I have a Schrader valve cap with a core tool on it in my car. None of my bikes has Schraders now.

CliffordK

I have broken pump heads in the past. Usually on portable mini-pumps. It is are, but one can normally feel the air coming out around the broken, or leaking head.

A hole in the tube is at the top of the list, but pumps do go bad too.

ricecrispies

I have removed the tyre and it turns out that the base of the valve stem has torn. I had put the rim tape all around the rim except for the 1 cm around the valve hole. Should I have somehow arranged the rim tape to go around the valve hole?

Retro Grouch 

What kind of pump are you using?

Some pumps look like a stick with the chuck attached rigidly to one end. If you have one that's like that you should be very careful to hold the pump head firmly against the tire as you pump. Otherwise you will eventually tear your inner tube at the base of the valve stem.
Some pumps have a hose that connects the pump to the tire. The benefit of that is that it uncouples the pumping motion from the valve stem.

CliffordK

Usually one tapes past the valve hole with a hole in the tape. You might make sure there aren't any particularly sharp spots at the hole.

Was the valve completely straight, or was it crooked? How much?

leob1

To answer your question, yes.
But you want to be sure that there is no burr or sharp edge around the valve stem hole. It's quite common for the to be a harp edge around the hole. A few seconds with a piece of fine sand paper will remove it.
Happy trails.

ricecrispies

I'm using a pump with a flexible connector, although it's rather a strange one because the end of the connector doesn't rotate so I have to turn the whole pump to connect it.