You might want to re-run the update then post the first few lines of the
hts-log.txt file here.
That way the people trying to help can tell which options and settings you are
using to see if it's a problem with those.
What you described sounds to me like something that can only happen if you
have set the options to do it that way. I think by "dynamic" links you mean
"external" links, i.e. url's in the downloaded copy of the site which point to
*external* or non-local pages. Not to nit-pick, but I was confused by "links
became DYNAMIC" in the subject. IMHO, a dynamic link is one which changes to
something different each time a page is loaded. But I digress...
Get into the hts-log.txt file after an update and select the text ABOVE
"Information, Warnings and Errors reported for this mirror". Copy/paste that
here and it will be a huge help to troubleshooting for you...