Firefox 3.6.8 says there are not updates but Firefox 3.6.9 does exist.

There have been a few people reporting they can not find the update. You can download the full setup file and install it on top of your current version instead.

OK that may get me the update, but why does my Firefox 3.6.8 fail to find the update? Is it Firefox, my PCs (two of them) or my ISP?

I don't know the reason why some people can not find the update.

You can try "Reset all user preferences to Firefox defaults" on the Safe mode start window.

You can also do a check for remnants from a previous update.

See http://kb.mozillazine.org/Software_Update (Software Update not working properly)

Remove the files in the updates and updates\0 folder.

The above solution is when a software update fails. I can't even get Firefox to try to do an update, as it thinks there is no newer version. And I checked a third PC of mine that was at Firefox 3.6.6 and it also tells me that there is no update.

It is highly unlikely that three PCs (and not all at the same level of Firefox) would fail identically.

I think there is a problem with the Firefox update website.