In my experience it depends on the website, its purpose and its technical procedures. The most accurate website will be the MLS, which is updated by the listing agent right after the settlement. MLS WOULD BE THE PRIMARY and thus THE MOST RELIABLE SOURCE OF INFORMATION. If your realtor sets an e-mail alert for you from MLS for a particular property that you are watching, you would be able to receive the news within a few hours (sometimes within a few minutes) after the update. All other websites use the MLS to generate "their" property reports. Some of them upload the MLS information on a daily basis (usually at night); most of them take 48 to 72 hours. There could also be websites, which "keep the property active" for 30 days after settlement. Why? Most likely because of either their poor technical support , or in attempt to generate more hits on the website and in this way generate more leads for the sales agents (this approach is used by a lot of web based sales brokers). It could also be a combination of both. I agree with you - BUYERS DO NOT WANT TO SEE SOLD PROPERTIES LISTED AS ACTIVE. However, over 90% of online viewings are done by the buyers who are just familiarizing themselves with the market and are not ready to purchase yet. They want to get a feeling of what they like and to preliminary estimate how much they are willing to pay for it. And various websites meet this need - they provide general information about the market, the area and the types of homes available in this area for such and such price.
All the best!