Bicycle Tutor

I'm looking for a solution. Getting tired of fixing flats.

What kind of rim - MTB / road?
What kind of valve.?
Where does it cut it?

I'm no expert but if I were you I'd be looking at my tyre pressure, probably needs to be increased. Check on the tyre wall for max. pressure and inflate accordingly. I had this problem once, the tyre was spinning on the rim and breaking off the valve stem.

Cheers.

Look at the valve hole in the rim. If there are sharp edges they keep cutting your tube. Take a large drill or a file to "break" (don't know appropriate English term) the edge. Also check if the rim tape is seated correctly and the valve hole is not too large.

Assuming you are fitting correctly, the commonest cause of tyre slip and subsequent damage to the valve is under inflation, read about it here, page 25.
http://www.schwalbe.co.uk/shopdata/files/TechInfo2-GB.pdf