I've noticed this issue has been around for a while now and according to others I've asked about it, it isnt just in cs 1.6/HL1 engine.
The issue is that when playing maps outside of the standard cs 1.6 maps inferno/nuke/dust2/italy etc... people get this strange error upon map change.
Pretty much it errors only SOME people from downloading new maps + resources and prompts a message such as.
Server build
connecting: IP can't continue without maps maps/de_mapname.bsp
but.... the OTHER half of the server downloads and gets in normally.
I've had this happen to myself as well and the fix to the issue is to reload your cs 1.6 and rejoin the server and then you go through the fast download process properly. The problem is not everyone reloads and rejoins... and this causes you to lose a good amount of your player base.
There are some things like cl_allowdownload "1" that people have proposed.. but I can vouch for the fact that it doesn't any role setting it to "0" or "1" as I've tried it with both.
I host with NFOservers and.. I doubt it's anything on their end. I also notice people get in on maps like fy_snow and other custom maps like de_mirage without issues... but then when u have maps with a couple sounds or models.. this is where some players are being kicked out the download and some arent... strange.