Tingling/numbness in any extremity is usually caused by a lack of blood flow to the tissues and /or nerves supplying them.
I have done a bit of personal anatomical research on this issue as I'm interested in bodies (well Matron, that's my excuse )
If you look at the diagram of the arterial circulation to the hand below you will see that the blood gets to your hands via one of two main arteries. One on the left and one on the right.
I believe that the position of your hands on the grips over a period of time causes a restriction of flow in these arteries and hence the tingling - which is simply the start of numbness.
If you allow the flow to return via just one of the arteries the tingling goes. You can do this (stangely) by gripping a bit tighter with your thumb, index finger and middle finger and lifting the heel and side of the palm off the bar. Therefore you do not have to lift your whole hand off the grips which may not be desirable at the time.
This (I believe) is due to the fact that one of the arteries is allowed to reflow and supply the tissues, ending the numbness.
The above explanation may be a crock of sh*t - but it works