Because collagen does not react with water and you say, no (measurable) evaporation of water is evident, there are only two options as to what is happening:
Matter is converted into energy: If virtually no evaporation or spillage took place, and your scale is working properly, this is what must have happened. Using the formula of mass-energy equivalence $E=mc^2$ (E = energy, m = mass, c = speed of light in a vacuum) we can calculate the amount of energy that should result from a "loss" of 2 grams: $$ E = 0.002~kg\cdot(2.998\cdot10^8~m/s)^2 $$ $$ E = 0.002~kg\cdot8.988\cdot10^{16}~m^2/s^2 $$ $$ E = 1.798\cdot10^{14} (kg~m^2)/s^2 = 1.798\cdot10^{14}~J$$ so... that would be a LOT of energy.
Your scale is not working as intended.
I'd go with option 2.
Now on a serious note: We do have a scale (precision of 0.0001 g) in our lab that occasionally has the same problems. Sometimes I would measure an empty reaction flask and it would be fine but some other time I could watch the measured weight drop by the second, "losing" up to 100 mg. The scale was checked by a professional but he could not find anything wrong with it.
My advice is: try another scale, see if the problem persists.