There are so many places to post race results online. Seriously, a multitude of websites will "host" the race results, the bigger ones being these three:
There are also all the other regional/national companies that handle the chip timing. Often these companies will post the results on their own websites for posterity.
The running club will also post the race results on their own website for future reference.
Now, that being said, the results that are posted on the first three sites will probably be there almost indefinitely! If a chip timing company fails, the website will fail. If the running club determines not to continue posting an older race, they will remove it. Just be forewarned....if you want to keep your results indefinitely, print out the club's/company's results for yourself. If its on Athlinks, Cool Running or Active, you can rest assurred that it will not simply go poof one day.
There are also a few sites that will post race results even for races that they do not properly host. Running in the USA is an example. But regardless of where its posted, just remember that no company is required to keep your results online forever...hopefully its on one of the bigger sites which host a ton of international events. But if not, save it yourself!