Hope you sealed the travertine when it was forst installed. You will need to renew the sealant at least every 6 months. Not cheap but it will prevent ugly stains and discolorations from "setting" into the porous stone.
The travertine was installed about 6 yrs ago. I just had it professionally sealed about 3 months ago. Will washing it with dishwashing soap every week wear it down sooner?
Dishwashing detergent might be one of the worst cleaner to use. Not because it'll wear the stone, but because it produces too many suds and will leave a dulling film. Find a cleaner that is intended for stone, it'll also have the right ph so no damage.
Great advice Jaz. Most people do not realize travertine is a kind of marble stone. Unlike procelain or ceramic, it is porous and subject to damage from what gets spilled on it.
You need to use a neutral cleaner, stonetech makes a product called klenzall, this will clean your stone, you will then want to seal the stone at least once a year for maximum protection