What can be done to deal with the increasing problem of stalking?

Sadly, really nothing could be done. The last thing these criminals think (I think), at the moment of committing a terrible crime is "but the law says this is wrong."

If I can have a non-Japanese approach to this issue, I would recommend taking a more active approach, such as considering eye witness testimony, cctv footage or even captured footage by the victims themselves. Another more aggressive take is to report potential cases to police and have some plain clothes officers tail them as a counter-stalker measure of sorts. I'm not knowledgeable with the Japanese law so pardon my ignorance.

1 warning, 2nd time = life sentence. If a stalker wont stop after 1 warning then they never will and almost certainly will be committing a heinous crime. Better to immediately lock them up for life.

Is there some evidence that it's an increasing problem?

As a counter measure for stalking, building a good relationship with neighbors on which we can rely in a community. Having an attention from neighbors will keep stalkers away from us. However, more and more people prefer keeping personal space to opening social space, which is unique to Japanese culture. Therefore, the bonds between one person and the other is getting thinner and smaller, compared to those decades ago. Building a person to person connection in a real world can be the best way to protect us from stalker.

Having an attention from neighbors will keep stalkers away from us. 

What if your neighbour is a stalker?:D

Improvement for reporting crimes and criminal behavior in Japan will help some.