It is safest to use this conjunction only in its temporal sense ("Your letter came while I was away on leave"). That does not mean that it is wrong to use it also as a conjunction without any temporal sense, equivalent to although ("while I do not agree with you, I accept your ruling"). But it should not be used in these two different senses in the same sentence, as in:
While appreciating your difficulties while your mother is seriously ill . .
Moreover, once we leave the shelter of the temporal sense, we are on the road to treating while as a synonym for and:
Nothing will be available for some time for the desired improvement, while the general supply of linoleum to new offices may have to cease when existing stocks have run out.
There is no point in saying while when you mean and. If you are too free with while you are sure sooner or later to land yourself in the absurdity of seeming to say that two events occurred simultaneously which could not possibly have done so.
The great Ohio flood . . . in 1937 which attained a height of over 65 feet developed in a week, while the almost identical amount of rain of the previous year produced a high-water mark of no more than 39 feet 3 inches.
H.M.S. Consort is due this morning in Shanghai while H.M.S. London was steaming last night upstream to help the Amethyst.