It's time to change strings when... it's time to change strings.
In all seriousness, it depends on the player, the strings, and the needs dictated by the player's performances.
With play, and contact with the oils in our skin, strings lose their edge and richness over time, even if you keep your hands clean when you play. So a prominent orchestral player might usually replace strings at least once a year. Meanwhile, I've got jazz players who come back for a new set every 6-8 months. And I've got bluegrassers in North Carolina who have the same strings on their old Kays that were on them when they bought their basses 20 years ago.
Signs it might be time to change?
- A broken string is a dead giveaway.
- Strings that are starting to unravel/unwind/get really crusty or grungy, etc. are usually a good sign that new ones might be in order.
- Strings that have lost their "verve" and don't inspire you as much anymore because they sound "dead."
- Strings that have a buzz to them, or whose sustain has suddenly become drastically shortened, often have a broken internal winding (one of the windings inside, which doesn't cause the whole string to completely fail, but definitely affects its tone and playability.) That's a good clue that you need to replace those strings.
- If strings start sounding out of tune - older strings can have their harmonics go "out of whack," so they start sounding out of tune (even though you KNOW your finger is in the right position). So that's a good sign as well.
But really, there isn't a specific interval where one "has to" get new strings - the need for a fresh set is dictated by players' needs, and for every player, that threshold is a little different. If they "sound good" and they "play good" - they're still good!