In my experience I have found a few things cause the slow down and login behaviors raised by the original question.
Slow downs - may be caused by potentially performance configurations by the SharePoint admin (for ways to get the server changes made ref: Fine Tuning Your SharePoint 2010 Environment – Front End Optimizations) ; or by having lists with membership changes where the list no longer has (or percieves to have) valid users referenced by the list items (people or group pickers); or if you have a bad list ( or corrupt one) and the SharePoint reference is getting lost becuase it can't find home.
Login issues associated with Slow Downs - may be caused by one of two network configurations. The first is manageable by the end-user and that has to do with setting or confirming you have the proper trust relationship for your Browser to communicate with SharePoint.
Under the IE (presuming this is the dominant default browser) Select -> Tools -> Internet Options -> Security -> Local intranet -> Sites -> Advanced and make sure your SharePoint domain is in the list of approved sites. You can use a wildcard such as the following *.yoursharepointsite.com like *.ibm.com if your sharepoint site is structured like sharepoint.ibm.com. This will tell IE to pass your credentials properly to the site because it "TRUSTS" it.
The other solution for login related Slow Downs can be provided by your Network team and insuring that as a user and a local domain you can trust reach the site withing your network (DNS ROUTING and DEFAULT CONFIGURATION do not have this set up).
The question with any solution is whether it addresses the initial problem.. without crystal clear example of what the problem is we're all just shooting at a percieved target with what we hope is useful.