1. Go to tripit.com
2. Enter your email and password into the login box on the top right corner. Do not select the "Remember Me" checkbox.
3. Click Login
-> It now takes you to another log in page with no message about why. The new page's URL is http://www.tripit.com/home
4. This time enter your email and password into the log in box in the middle of the page, make sure you do not select the Keep me Logged in checkbox
5. Click on Login
-> If you're lucky, it will log you in the first time, if not, you'll have to repeat steps 4 & 5 two to three times
6. Now try to edit a trip, for example, add a flight to an existing itinerary.
-> When you click on Add, it takes you back to the login screen that showed up after step 3.
7. Login again (do not select the checkbox)
8. It returns to the edit screen, but your changes have not been saved. Repeat step 6 and if you're lucky, it will go through, if not you have to go through this flow a few times.
I contacted tripit customer care about this a while ago, though I didn't have it in so much detail. They asked me which browser I was using and I haven't heard anything from them after I replied.
They're now offering Pro services, but I'm definitely not giving money to a company that can't even handle something as simple as a login screen.