This is not my field but from a gardeners prospective if you are experiencing a problem with the growth of green algae then I would suggest the following for consideration:-
Contamination of the medium. the vessel used to contain the medium or from the surrounding environment.
Insufficient nutrients. light or heat.
Bacterial contamination.
Foreign body contamination.
Incompatible element between medium and material in contact with medium
It is difficult to guess without knowing the algae type and growth conditions. But you should start checking the pH first. Light may be a factor, but usually in a well lit condition in the beginning, it should not be a problem.
I believe you are not be using the best culture medium for growing greens. Guillard and Ryther’s F/2 medium was developed as a seawater medium designed for growing coastal marine algae, especially diatoms with both silica and vitamins added to support their growth. The best medium for growing greens has been Bolds Basal Medium (BBM). Years ago, Harold Bold of the University of Texas and his students used BBM for isolating and culturing coccoid freshwater green algae. Others have since used it for this purpose. Based on your use of the F/2 medium, it appears that your goal has been to culture estuarine/brackish water greens. If so, I wonder if anyone has prepared BBM using seawater at various strengths for this purpose. I know of one paper that has used BBM without seawater for this purpose. Thirty years ago, I believe Guillard and Bold collaborated using BBM for the successful culture of estuarine coccoid greens - several of which were described as new species. You may want to explore this as an option for culturing brackish water greens.
As I know, many green algae are freshwater species. f/2 mediun is better for marine strain. In my lab, BG-11, BBM, BM are commonly used for cultivating freshwater green algae due to higher nitrate concentration.
It might simply be due to nutrient-limited growth, since several greens require high nutrient concentrations. I would try a sequence of f/2, f and 2f (namely, doubling the concentrations of all nutrients). I would also use George' s suggestion to try several salinities, from fully marine to freshwater. Using your own results, you may then refine the requirements for each one of your strains.