My guess is that they are not a country with much sports diversity. Previously (until 1936) they were a superpower in T&F, especially in middle and long distance and javelin. In middle and long distance running, the east africans came and ate their lunch. They had no male javelin finalist this year, while Kenya, of all places, had one. He had trained a lot in Finland, though. A look at the wiki page of Finnish medalists since 1992 shows that most of those have medaled in old sports. In recent years, the games have diversified a lot by adding a lot of new events, but Finland has not helped itself to those opportunities, by and large. The 2nd most medaling sport for Finland is wrestling, but there they have been losing out to a growing importance of countries in the area that formerly was covered by either the old Persian Empire or Ottoman Empire.
The common theme of those events is that it is easy - conceptually - to dope for them, and Finland is probably not willing to compete in that regard.
The last superstar Olympic Finn was distance runner Lasse Viren in the 1970s who was subject to numerous allegations that he would have some of his blood stored during the off-season then would get topped off with a pint or two right before the Olympics.
Also, none of those sports pay anything unless you reach Olympic medalist status, and not all that much even then. Until the 60ies, when a lot of Finns were poor, it made sense to train hard in the off chance that the training provided a way out of the cold farm. Look at Michigan upper peninsula - a lot of finns emigrated there, and it is the only place in USA where finns dominate. It is also a cold place, and the agricultural land is not bountiful. Now, Finland itself is to a great part even bleaker. Do a google pic search of Finland before 1960. Now, Finland has undergone a huge economic leap forward, so it makes more sense to study for getting into Nokia rather than to escape the farm. That economic logic is not there for a Kenyan runner or Taijik wrestler.
Finland would do well by following the British lead. GB had their best games. medal-wise, since 1908. GB performed exceedingly well in Equestrian, rowing, and a few other sports. The commong thing about those 2 sports is that they cost quite a bit to compete in, so there are significant barriers which limit competition from poorer countries.
Finland has the sports mix of a poor country, with a 5 million population, and rich people. That is not a good combination if one wants to amass a lot of medals.