I just posted some recipes yesterday in another thread about DIY mixes for Hagen systems. I have also not been able to match the longevity of the Hagen mix in the same volume.
The volume of the container of course makes a big difference. If your mix only lasts a week there is something wrong. I have not tried 2-liter bottles yet. After this latest battery of recipe longevity tests, I may give 2-liters a try, as they should last at least 1/3 longer than the 1-liter mixes.
My recipe for Hagen canister which is .5 liter (lasts 2.5-3 weeks for me):
-1/2 cup sugar
-1/3 tsp champagne yeast
-1/4 tsp baking soda
-water, 60-80 F, filled to just below curve of bottle, stir contents gently
My recipe for 1 liter bottle (lasts 4-6 weeks for me):
-1 cup sugar
-1/2 tsp champagne yeast
-1/3 tsp baking soda
-water, 60-80 F, filled to just below curve of bottle, stir contents gently
Also, some have said that leaving the sludge in the bottom after pouring out the liquid in a spent DIY mix would help things start faster and go longer. I have not found this to be of any real benefit in either respect thus far, however. Most of my mixes start bubbling within an hour or so.