Importing financial history into mint.com

I've noticed what you're describing as well. At least with some sites, if they provide two-factor authentication, they ask you to verify factors beyond username/password from time-to-time. Generally, I've been able to resolve this by going to the site manually to verify my additional factors. Then when I refresh, the information updates again.

Two-factor security seems to be more and more prevalent with banking sites. I know Citibank does it for their student loan website. Vanguard does it for their site as well. Chevy Chase Bank (now owned by Capital One) does it on their website too, but I haven't had any update problems on that account with mint.com.

Here is an instruction of adding ING Direct account (by eHow).

And, seems that some people are having the same problem as you.
So, in case the above instruction didn't help, below is the solution suggested by mint.com.

Stephen_Mann, Official Rep, replied on January 12, 2010 16:32

We have been seeing very good success rates over the past month. If you are having problems our first recommendation is to try outside of normal business hours in the US, for example before 7am PST and after 5pm PST. Otherwise, please file your issue directly with Mint Customer Service as we are not experiencing any ING wide issues at this time