I vote for keeping it monthly.
I don't think it's necessary to have the challenges race by at breakneck speed, with a flurry of entries followed by a flurry of votes, and then more of the same.
Most of the entries have come early in the two contests we've run so far, that is true -- but it may not always be the case. Some good entries have come late, as well, and we may have missed out on those. Not everyone is able to enter early. Sometimes, people will be busy. They may have an idea simmering throughout the month, but only be able to enter it near the end.
I don't see why we need be in a rush to get on to the next challenge. As it stands, there is ample time for reflection and consideration -- both for people wishing to enter, and for those considering where to place their vote.
I think that's a good thing.
For example (this isn't my reason for thinking as I do, but it serves to illustrate my point), next month, I'm going to be away from the 3rd to the 10th, and again from the 14th to the 18th. I shall try and craft my entry during that time, but I may not have the opportunity. If the challenge is reduced to three weeks, I may not be able to enter. Personal circumstances dictate that my entry will come later, next month.
With a monthly challenge, everyone knows where they stand.
With a different format, I have a feeling we'll end up getting fewer entries, and fewer people voting. People will lose track of when the current challenge ends, and when the next one begins.