Sodastream loses carbonation when adding syrup
The solubility of carbon dioxide in water is a function of several factors. The most important are time, temperature, pressure, and composition. 


In order to maximize your carbonation, ensure everything is as cold as possible. The colder the liquid, the more CO2 you can dissolve in the liquid.
Secondly, you will need high pressure. The higher the pressure the more CO2. For example, if you leave an open bottle of carbonated water on your table, it will go flat. If you cap the bottle, it will maintain carbonation, but also build up pressure in the bottle. The higher the pressure, the higher the carbonation. Any "other gasses", like atmospheric oxygen and nitrogen in the bottle will effectively reduce the "partial pressure" of CO2, so you should remove that. 
Pure water is easy to carbonate. Once you start adding "stuff" to it, it becomes more difficult. Soda concentrate contains flavors and sugar, all of which hinder the ability of CO2 to dissolve into the the liquid.
It takes time for the system to reach equilibrium. If one just pressurizes a bottle with CO2, it can take quite a while for it to actually dissolve into the liquid. Increasing the contact between liquid and gas (the surface area) speeds up the dissolution.


I don't know how a sodastream works, so if my suggestions can't be exactly duplicated, let me know. Can you add CO2 to the bottle without opening up to the atmosphere?
The best process would be to, first, ensure everything is cold, and mix everything together. Pressurize the bottle with CO2. Cap it to maintain pressure and shake...a lot. Purge the pressure to remove any oxygen and nitrogen, and repressureize. Close the bottle and shake again and you'll notice the pressure decrease as the CO2 dissolves (squeeze the bottle). Top off the pressure and keep shaking and squeezing and repeat until it stays pressurized. Allow any foam to subside, and make sure there are no bubbles on the wall of the bottle before opening.

I make a lot of soda, but use a large cylinder of CO2 and Carbonator Caps, which screw on standard plastic soda bottles. With this I can make anything from 12 ounce to 2 liters at a time.