How long will a Thai dressing keep in the fridge?
This particular dressing, unlike others that carry a botulism risk, only contains water soluble components. Oxygen will always be able to dissolve in here and prevent the botulism conditions, unless there is a TON of garlic at the bottom.

Garlic botulism risk comes from creating an anaerobic environment, where the bacteria can act under a protective blanket of oil, without oxygen from interfering.

The components you mention all are used in other instances to retard bacterial growth. Low pH for acid, sugar, and no oil. I do not have good data on whether capsaicin is a preservative, but it is certainly not a big risk.

Over time, since these components are exposed to Oxygen, there will be degradation of the flavors due to oxidation, but there is very little food safety hazard. The 60 mL fish sauce is so salty that bacteria don't stand a chance. 

I keep, and have an Indonesian friend who has a similar jar out at room temp all the time. Lime rinds and garlic peels and odds and ends in that category go in it all the time and it is a staple.

That all being said, every precautionary guideline will say to follow temperature danger zone recommendations, so we also have to understand our bodies and immune systems.