One reason for ecology losing its holistic character is probably funding - you don't get funded for a holistic approach - you get funded for small, simple, verifiable results. The holistic putting-the-pieces-together is the task for after hours ..

Is it just an issue of funding or more than that an issue of thought process and the methodology of science - that divides an issue in to fragments ?

Ecology is a holistic science, however to bring holism to an ecological phenomenon one need to understand the underlying complex processes. Many researchers are trying to understand the processes. There is always a scope for putting small researches into bigger perspective to bring holistic picture of a ecological phenomenon. Probably we are missing such visionary ecologists who can really stitch together the small, simple, verifiable facts being investigated on routine basis. 

But, I have an issue - does reductionist method drain-off the spirit and content of the holistic perspective?

I don't think so. The other side of the coin is, there is always a fear of loosing the exactness in certain processes when holistic perspective is discussed. I also believe that while working on a narrow problem, holistic perspective for which the study is being conducted should not be forgotten. In nut shell, progress can not be made without cracking the complex and small problems (for which funding is available as mentioned by Susanne), at the same time holistic perspective should always be there as guiding force and no one is paid for doing that except some Emeritus professors.

I think holistic studies needs to transcend the Cartesian framework, to understand the whole functioning; when you divide some thing sometime the functionality is lost; a flower is not just its parts and painting is not just the paints and the colors, an ecosystem is not just the bunch of species or non-living factors, a living body is not just the organelles; but in case of man-made gadgets and technology there is not other way except looking at the parts or designing the parts to make a larger system

But, I think Mathematics helps to grasp the facts in much better and holistic manner; I do not think that the tools of maths will cause lose of fuller understanding; see for example system models

Mathematics may well "help to grasp the facts in much better and holistic manner", but as soon as mathematical models are that complex, they are not that easily approachable by (most) ecologists, OR philosophers, anymore, I guess - any ecologist can easily deal with a simple y = ax + b model, but when the mathematical model covers pages after pages (in order to represent (most of) the complexity), it takes a lot of effort to still understand every single line AND see the holistic patterns underlying. Mathematics might help, for sure, but it might not be the easiest path .. However, it might build a concrete picture - but then again the discussions would start on every single parameter - and those discussions would very easily lose any holistic picture 

any model will always "only" account for a part of the explanation, otherwise it would not be a model but an exact description (model or description might be done using mathematical tools .. ) - an exact description is rather unthinkable in biology because we still lack too much understanding .. But of course the given part might be minutely small or close to 100% of the complete description. But I am not even sure whether we all mean the same thing when we say holistic? Is the complete description of all phenomena holistic? Or does holistic not also include something beyond the complete description - does the holistic approach not necessarily have to involve meta-physics?

Model, of course is only first step; then it has to grow to represent the real. 

Apart from complete description, there has to be component on perception. Science has to grow up with new and innovative tools to capture holistic understanding of nature and its numerous phenomena and it surely will do. But it needs also change in our attitudes and perceptions; many a times science has grown under the patronage of certain interests, examples are many; But the knowledge has to be owned by the society at large; issues related to intellectual property rights and so on so forth distort its development.   It needs a change