Why there is no single number
Every floor takes a different amount of use, and grout is porous, so what matters is how fast soil gets into it rather than how many months have passed. A guest bathroom and a kitchen in the same house are on completely different schedules.
We could give you a figure that sounds authoritative. It would not be true of your floor, and you would either clean too early and waste money or leave it too long and lose grout color permanently. Reading the floor is more useful.
What to look for
Run a damp cloth over a grout line in a part of the room nobody walks on, then over one in the main traffic route. If the two now look different, the difference you were seeing is soil, and cleaning will take it out.
If the traffic line stays darker when wet, the soil has gone into the body of the grout. That is the point at which professional extraction is worth booking, because it is still recoverable and will not stay that way indefinitely.
If it stays darker and a sealer was applied not long ago, the sealer has failed rather than the grout, which is a different and smaller problem.
What changes the interval
Shoes indoors. Grit is the main thing that damages grout, and most of it arrives on footwear. A house where shoes come off at the door is on a much longer cycle than one where they do not.
Pets and children, for the obvious reasons, and because spills that sit are what stains grout through rather than merely soiling it.
Hard water, which is a given in the Valley. Mineral deposits build on grout as well as in it, and they hold onto everything else that lands.
Whether the grout is sealed, and how long ago. A working penetrating sealer keeps spills on the surface long enough to be wiped up. Once it stops doing that, the interval shortens sharply.
Monsoon season, which pushes fine grit indoors for weeks at a time. A floor that was fine in spring can look tired by autumn for reasons that have nothing to do with how you cleaned it.
The thing worth not leaving
Grout that is soiled cleans up. Grout that has been stained through its body will lighten rather than return to its original color, and there is no cleaning method that changes that. The gap between those two states is where a professional clean is worth most, and it closes gradually enough that most people miss it.
Ultimate Floor Care cleans tile and grout at $0.35 per square foot across Phoenix, Peoria, and the West Valley, and a penetrating sealer adds $0.15. Estimates are free, so if you are unsure where your floor sits, it costs nothing to ask.

