We are frequently testing this feature and have never encountered any bugs with it.
I checked your site and it looks like the problem might be with your domain setup - so your members can't use this feature in the first place to reset the password.
It looks like your site is setup for primary domain : http://www.youreagleteam.com
However this domain redirects to your WA site http://youreagleteam.onefireplace.org - instead of pointing directly to WA servers as described here: http://help.wildapricot.com/display/DOC/Custom+domain+setup
As a result, links to events, reset password etc. would not work.
You need either to change your domain setup - or set primary domain to WA one.
If this does not solve your problem, let us know.
Dmitry Buterin, Chief Apricot