If you give us a brand of string you're using, we can speak to our particular experiences with that brand.
On my viola, it's actually very easy to tell when I need new strings, because I use a mixed set of two different brands (Larsen A, Vision for the other strings) and they go dull at different rates. When they're in good condition, the two brands match extremely well on my viola. When I start noticing a mismatch between my D and A strings, and having to adjust my bowing technique to maintain phrase shape across the two strings, I know it's definitely time to change strings.