Best not to host the videos locally, then. There are a number of services which will host files for free, so upload to them and just link to them from your own site.
I don't know all of the limitations that each of these sites might have, but you will almost certainly meet your needs with one or other of them.
RapidShare
I'll Host It
Filegone
Putfile
...or just peruse this list :)
Some sites will delete files that have not been downloaded for a certain number of days. As a workaround you probably need only hit them momentarily, and could do so by opening a set of bookmark tabs, then cancelling each download in turn, which would be a small task to remember to do once or twice a month. Paid memberships probably eliminate this sort of issue, OTOH.
Of course if the problem is really only in the month or two after a new video is released, then you could probably safely revert to local hosting after the other site has handled the bulk of the traffic for you, and not need to worry about keeping tabs on a large number of exernal files.