Wondered where you had gone - thought maybe you were on a cruise or something like that, or maybe on a buying trip to some foreign country to smuggle in some Freon after hearing the scare rumors on web blogs about R-22 running out of availability this summer due to lower production this year thanks to the EPA.
The good news - the AL system still knows you, because your answers are still on the Leaderboard, so all your good answers in the past are still there for people to see.
The reason it is taking you to the login/logout page is it does not recognize you as a user - so you might have cleared your cookies in the browser, or changed to a different browser or computer if it is not remembering you. Or turned off acceptance of Cookies.
One other thing I have noticed - get too many AL cookies or cache entries and it takes forever to load or times out and dumps you back to the logout/login page - maybe you need to delete the Cache and Cookie entries that originated with Angies List.
IF the following doesn't work you will have to contact member services - but AL log-in has a known glitch. If you answer a question without first logging in, after you enter the answer it pops up the log-in page - with new member registration area on the left side, returning registered uses/member on the right side which is where I presume you are entering your user name and password. Now the glitch - the webpage does not use cursor tracking, meaning it does not keep track of where the cursor (mouse icon) is (due to clicking or tabbing) - so if you hit Return or Enter after entering your password, it thinks you are on the left side of the page registering as a new user and of course all the fields on that side a blank because you are not using them, so it dumps the answer and returns you to the logout page.
The work-around - after entering username and password on the right side of the page, CLICK on the button below the Password box labelled Login rather than hitting return or enter - then it should work - at least it does for me. This glitch has been in the system for a couple of years but they have not fixed it.
Or log in each time before starting to answer questions.