There's a version of this which has 1 part sugar, 1 part nuoc mam, 1 part lime juice and 2 parts water--I prefer it tastewise, but be aware that it's more fiddly to put together and slightly more unforgiving of dosage errors...
My grandma says it'll keep for two weeks; experience has proven it can keep for far longer than that (basically, this is an acid and salty milieu in a cold environment. Bacteries shrivel and die before they can get a proper foothold).
If you're NOT using 35° fish sauce (and if your bottle of nước mắm carried no inscriptions, chances are you're using the US standard of 20°), adjust by 20/35.