Searching on the Internet one can find a lot of occurrences of "all year round" and there are plenty of sites which explain what the expression means: throughout all the seasons of the year.
So, one would expect that "all [x] round", where [x] is day, or week, or even month, would be well established, too; but that is not the case, at least judging from Google results, which show the use of "all day/week/month round" mostly in some illiterate comments.
It's easy to deduce the meaning of "all week round" as "throughout all the days of the week". Can this expression be used like this? If not, why?
Best Answer
I think this is a problem, if you want to call it that, about collocations. Fixed expressions such as: "all night long", "at the weekends" ("on the weekends" if you are from the US), "year in, year out", (oops that an idiom!) and "by day/night" are instantly recognized and understood. For example, it is perfectly acceptable to say, "all year round" but I would never say, and I don't think I have ever read: "all month *round". Why can't I or you say it? Well, nothing is physically stopping us, but as an expression it sounds odd to the native ear.
What's even worse for language learners is that English does insist on evolving, despite our feeble protests and what was once considered inappropriate, grammatically incorrect and illiterate, is now accepted usage. So who knows if enough people start saying, "all month round", then maybe that expression will become fixed in time through repeated exposure.
The link I posted is actually quite neat, it lists all the collocations with "day" by courtesy of the Oxford collocation dictionary. A dictionary which I was totally unaware existed until tonight, 23/7/2013. So thank you, Carlo for your question, which made me do the research and discover this little gem. (See, yet another another collocation, we don't normally say: little jewel!)