There are many techniques available for studying the stability of clay-humus complexes like synchrotron-based XENES techniques but i don't know about the availability of this instrument in India. various works are being done by Lehman and Solomon on this aspect whose papers are available on the website of Cornell university which may be helpful to you.
These question may be interpreted in two ways: (a) do you mean 'chemical stability'?, or (b) do you mean 'biological stability'? In my opinion, within a soil the main driver of change is the soil biota, and most particularly microbiota (bacteria, fungi, archaea, actynomycota). Thus to me the most relevant (and realistic) way of measuring how stable is a clay-humus complex is to incubate it under standard conditions.
I understand that you have already isolated the clay-humus complex. In this isolation process (using... ultrasonics? a dispersive agent such as Polyphosphate?) the very most of soil microbiota must have been lost (or died in the process). Another possibility is that you obatined 'synthetic' clay-humus complexes in your lab. At any rate, I assume that your complexes are devoid of native microbiota. Thus I suggest:
a) Mix your clay-humus complex with quartz sand, to provide a media more or less similar to a soil, with enough porosity to maintain water content but also to allow for a good oxigenation. Of course, the proportions sand / clay-humus complex must be fixed. Impossible to give you ideal proportions: you should perform some trials before...
b) Place this mixture in an open flask, and add an inoculum. The inoculum may be obtained by shaking a freshly-sampled, biologically active soil (say, the topsoil of a pasture, or a crop) with either distilled water or (better) a slighty saline solution (0.01 M CaCl2, for instance), and filtering the solution thereafter. The filtrate will contain a good amount of microbial corpses. Mix well the inoculum with the mixture sand + clay-humus complex, to ensure that the whole mixture becomes wetted.
c) Incubate this mixture (clay-humus complex + quartz sand + inoculum) within a sealed jar, with a NaOH flask. In other words: the classical method for incubating soil samples. You may find a lot of descriptions about the whole procedure.
Essentially, what you do is evaluate how much of the organic matter in the clay-humus complex is lost upon incubation. You may decide the incubation time needed for your purpose, but I think 1 month is enough to have an idea. Of course you must perform samplings from time to time.
Also of course, this is a comparative method; and the interest of such a procedure is that you may change a lot of variables and investigate how these variables affect the stability of the clay-humus complex. For instance, (i) temperature of incubation, (ii) clay type (montmorillonite, kaolinite, chlorite...), (iii) the intrinsic characteristics of the humus part of the complex (more or less aromatic, more or less rich in o-alkyl carbon...), etc.
Please say if you need more details about the incubation method.
I think for studies on clay-humus complexes in soil a dedicated laboratory,preferbly a Clay Mineralogy Laboratory with required equipment /instrumentation and a dedicted scientist (to that line of work) are required.My comment is based on the background of scientists who have worked in this line.I appreciate the comments of Drs.Chaudhary and Rovira.Apart from carbon sequestration,clay-humus complexes have role in soil aggregation (in turn soil structure),mobility and plant availability of micronutients and heavy metals.Apart from the factors mentioned by Dr.Rovira,the soil pH influences the nature of bonding in clay-humus complexes.The following papers and one review article may provide some basic information on clay-humus complexes to plan for more advanced work.Alternatives to very costly equipment may be available ( may not always) if one searches literature.
Study of clay-organic complexes .Review article by Manjaiah,K.M. et al. Current Science ,98(7)April 2010 www.currentscience.ac.in/downloads/article_id_098_07_0915_0921_0.pdf
Clay- humus Complexation:Effect of pH and the nature of bonding by Varadachari,C et al. Soil Biol.Biochem. 26(9):1145-1149 ,1994.
Assessing the stability of humus in soils from continuous rice-wheat and maize-wheat systems using kinetics of humus desorption. Datta,S.C. et al.2015 Commun.Soil Sci.Plant.Anal.46(22):2888-2900.