Yes, winning every month is possible and almost is necessary to be successful in trading. Sure, someone may make money 6 months of the year, and lose the other 6 months, so they would be breakeven in the end. However, would you really consider them successful? You have to remember that 95% of traders lose money anyways, so achieving consistent profitability every month can be difficult. Just because most don't do it, doesn't be its impossible or not important.
The way I see it, you have to come out ahead (or at least not too far behind) each and every month if you are day trading. Almost every week is also important. However, regarding the people that say you have to win everyday, I think that's a bit far fetched. Sometimes you or your method will just not work in certain environments, so its better to accept the losses and walk away rather than dig the hole deeper. So yes, losing days are OK and sometimes welcome. However, the majority of weeks should be profitable, which leads to almost a profit every month.