Hi,
I can't say about any research has been done on this topic or not. First I would like to quote whatt moz says about internal linking "Internal links are most useful for establishing site architecture and spreading link juice (URLs are also essential)."
I would like to break into two parts
1> If page/pages linked from blocked pages it means crawler won't find linked pages because pages are blocked from robots.txt this hinders their ability to get pages listed in the search engines' indices. I presume these pages blocked in robots.txt before migration so this could not be reason
2> Link Juice won't flow because it is blocked & it is blocked earlier too (before migration) so this also could not be the reason.
*** During migration website does lose ranking if website does not properly redirected so please check whether you followed best practice for migration or not by checking below URL
http://moz.com/blog/web-site-migration-guide-tips-for-seos
Thanks