We have always grown red onions, and this year, for the first time have grown white and the normal brown ones.
We grow Red Baron from Marshalls, and have found them to grow well (but not large) on both clay and peat soils, but tend to need pulling early as they are prone to attack from fungi both above and below ground. Have never been able to store them beyond Xmas either (and thats on a good year !). So I understand your frustrations!!
Interestingly this year of the 3 colours , they have done much the same as the others and a little better in size than the whites (but that could be the variety).
I'm sure it's nothing you are doing- perhaps the wrong variety for your soil type or how they are 'treated' by the company you buy them from??? Frustrating isn't it!