The #1 reason for increased number of children being orphaned is child abuse.

Children's Home Stats & Stories from homes

Here's some information we can check for new stats. recommended by Port Kanegaya (November 20, 2018).
I tried to simplify but there's quite a lot of data written in complex kanji characters.

1) https://www.mhlw.go.jp/stf/houdou/0000071187.html 
Data taken every 5 years by the Ministry of Health and Labour. Next one should be Heisei 30 (Feb 2018) but the data isn't there yet.

2) https://www.mhlw.go.jp/file/06-Seisakujouhou-11900000-Koyoukintoujidoukateikyoku/0000187952.pdf

This one is also by the Ministry of Health and Labor states the following:
The latest data - 2016 (Heisei 28) data shows that there are currently: 
615 children's homes across Japan 
Room for 32,605 children to live in these homes 
Currently 26,449 children living in these homes
Number of staff members: 17,137 (though this is not too helpful since it includes admin staff)
 
National data on children moving onto 4-year universities, 2-year college, or finding a job.
(dated May 1, 2016 - Heisei 28)
1,818 high school children living in homes    -> up from 1,543 in 2012
226 (12.4%) went to a 4-year university    -> up from 11% in 2012
211 (11.6% went to a 2-year college)         -> up from 11% in 2012
1,280 (70.4%) found jobs                           -> same as 70.4% (1,087 children) in 2012
101 (5.6%) are defined as "others"            -> down from 117 (7.6%) in 2012
* which means that number of orphaned children has increased and therefore the number of kids getting into uni and college have also increased, but the number of children becoming employed has remained the same.

3) http://www.metro.tokyo.jp/tosei/hodohappyo/press/2017/02/24/documents/09_01.pdf
* Data taken every 5 years by the Tokyo Government. next data should be 2022.

According to data taken in 2017, 87.1% of children living in the homes are employed,  up from 71.4% in 2012, so Tokyo is doing better than the national data. However, 46% of the job are in the service industry which would include restaurants, izakayas, karaoke stores, coffee shops, pachinko parlours, mobile phone shops (these examples were listed). 45% are full-time employees, 35% are part-timers. 12% temp staffs. More than 50% make less than 150,000 yen per month. 

https://note.mu/taejun/n/nd18ce7480911
Slide show recommended by Port K.  One important key info I thought was that the the #1 reason for increased number of children being orphaned is child abuse. 38% in 2013 up from 19% in 1998.