Hi,
I cannot login either (I had not realised as I don't use it)
However going to the Yahoo Site and changing the password does not do anything.
Using their "Less Secure Apps" option does not do anything either (there was an email saying I was using access to mail via a non secure app - but I have not used their mail service for a very long time.)
Having said that reading further suggests it is not Mail (after OS X 10.9 is OK)
It does not mention about accessing their Messaging service.
There is no option in Messages to try to turn Off SSL as you can with AIM or Jabber accounts
I have looked around the help pages (a little bit) but have found nothing yet.

8:49 pm Tuesday; October 4, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)