My understanding is that the ratio shifts from 10:1 (liquid to roux) for a pale roux, up to about 5:1 for a nutty brown roux, with a somewhat linear relationship between the two extremes. A dark brown roux has very little thickening power, mostly they are used for flavor more than actual work-a-day thickening.
The problem may not so much in the roux ratios, but in other ingredient variations. For instance, if you are using a traditional 3:2 flour:fat roux, and your fat is butter, make sure you are using clarified butter, or that you are allowing most of the water to cook out of the butter before adding the flour - excess water in the roux will break down some of the starches and reduce the thickening strength.
Finally, there will be some variation no matter what - you can always make a little extra roux in a second pan to integrate if necessary.
According to On Food and Cooking by Harold McGee, roux functions as a thickener due the starches in the flour swelling up and interfering with the flow of water.
In fact, he indicates that technique can be used with any starch and any fat.
This implies that a lower-protein flour (which implies higher starch, weight per weight) like soft summer wheat, or a cake flour will make a more effective roux.
As an aside: roux can be made with oil instead of butter. As we know oil contains no water, and gluten only forms in the presence of water, we know that roux functions without gluten, as there can be no gluten development in an oil-based roux.
McGee explains that cooking the roux initially increases its thickening power by cross-connecting some of the starches. However, as browning occurs, the maillard reactions are transforming starches and proteins into other molecules, and reducing the ability of the roux to thicken.
So yes, it is true that the darker the roux, the less thickening power it has.
In New Orleans style gumbos, for example, the roux is so dark (almost a mahogony color) that it adds no thickening power at all to the stew—it is there for the flavor. The thickening in that dish comes from (depending on the tradition followed) either file powder or ochra, or both (not considered traditional).
I was not able to determine an ideal ratio of flour to fat. McGee indicates that a 1:1 ratio is traditional. However, if that fat is butter, about 20% of it is water, so that really does leave more flour than fat after the water evaporates. In any case, as long as there is sufficient fat for the roux to be cooked smoothly, it will work fine. Additionally, the fat in the roux is also indirectly an ingredient in the finished dish, so it might be desirable in its own right, depending on the outcome.
Best Answer
You can visualise it like this: starch is the way that plants store energy, you can see it like long chains of glucose molecules. If you have these long chains, they lock in water at high temps (gelatinisation), and so they bind sauces. If you burn them, what you do is break those chains into glucose (or maltose), and that glucose you caramelise..that is what makes it brown...and the proteins are in the Maillard reaction..that is "caramelising" of proteins instead of sugars, but that is less relevant for the binding power of starches. So, you are breaking and burning the chains that you need to catch water, basically. (and please do not correct this text from UK to US spelling, thanks...)