One easy way to explain it is that Detective Conan happens on another planet that just happens to be very, very, very, very similar to the one we live on. This planet takes much longer to go around the sun than ours does, taking somewhere between 50 and 100 months (or possibly more) to actually do so. The planet wobbles on its axis a lot, meaning the seasons come and go many times in one year, with a new season appearing about every three months. Because the names of the months are based on the season cycle, and not on the year, there are only twelve named months, and each month will occur numerous times during the year. So, because the planet has yet to make it all the way around the sun, it makes sense that they haven't aged a full year in the series.
There's also a legend on this planet that the world and everyone on it was brought into being by a god named Aoyama, and he set the lengths of days, months and those really, really long years. Of course, this has since been disproved by science.
