I have an ADSL connection, verified capable of at least 250 KB/s data rate when downloading.
In attempts to download the virus database from within ClamWin, data rates, as seen
from the "bytes read" on the connection icon, seem about 50 BYTES/s (yes, bytes).
This is confirmed by the fact that, in one attempt, the download was not complete
even after a 12h period.
The ClamWin version I have is 8.8.5 and the OS is Windows 98.
I could not find in your site any directions for manually downloading the database. Is
there any way to do so ?

Please check out this FAQ : https://www.clamwin.com/content/view/58/27/.

You could also try to download from a different database server (see https://www.clamav.net/mirrors.html). To set the database server, open clamwin preferences > internet updates.

all mirror links in the
https://www.clamav.net/mirrors.html
redirect to the clamav.net home and
it seems that there is no way to
access a specific mirror for
manual download.
On other side, Explorer (Lynx too)
sees the pages
https://database.clamav.net/main.cvd
https://database.clamav.net/daily.cvd
as plaintext and try to display
them, instead of asking whether one
wants to download . This makes the
download still too slow to be
practical, albeit much faster than
the ClamWin auto download .

Do you have trouble downloading anything besides the ClamWin signature database? If you do, the problem may be on your end--maybe a firewall, etc. Do you have the same problem with ClamWin configured for automatic updates? See if you have it configured for a proxy. You might also try downloading the new 0.88.6 version of ClamWin and see if that helps.

Regards,