Winzip shouldn't cause an invalid archive problem, even if you have a demo version.
Do you have dialup or DSL or cable?
Where are you downloading the demos from? Always the same place or different places?
This may be your ISP's problem rather than your problem. But if you have dialup, some sites will cut you off if you take too long to download. A download manager may help if you have dialup, since it can download in segments and resume broken downloads. You have to watch out which download manager you use though, since some contain undesirable things as well as the download manager.