How big are these other sites?
From what I do at work and reading between the lines of what the admins have posted, it sounds like TBN is big enough that it is getting flagged as a spammer for sending too much (very similar) email out.
Just a guess here with some guesstimated numbers, but there are 134k users on TBN and if 10% of them get 1 email notification per day, that is 13,000 emails per day. If an additional 1% of the members are very active and get 5 emails per day, that is around 19,700 emails per day.
That is a lot of emails, enough to make AOL or Yahoo complain, especially if people go and hit the spam button to get rid of the message rather then the delete button (I see 1-3 of those per week for our domain from AOL users and we only average ~20 emails/day to AOL out of ~1000 emails/day that go to the outside world)
As for Yahoo, they are a world unto themselves and don't care what anyone else does. There is NO way that I have found for a small to midsize webmaster to contact them and get a real person to find out why their emails are getting bounced, or to report a Yahoo user who is sending 20+ spam emails per day to one of your users.
Aaron Z