Windows 7 - Site no longer opening autmatically: A cookie management problem?

My browser is Maxthon 2.5.18.1000 (runs off IE9's engine). My home page is my.yahoo (customized yahoo) and it is selected to open automatically when Maxthon is opened. For my.yahoo to open, I have to sign in with a username and a password. Until recently, my.yahoo would open automatically without my signing in. However, once I started fooling around with LastPass (a pw manager) and two other cookie eaters (CCleaner and Maxthon's Smart Cookie Cleaner), in order to get to my.yahoo, I now have to sign in. How do I get back to the state in which my.yahoo opens automatically without signing in?

If your browser uses IE's engine, perhaps an IE solution will work:
Opening web site without having to enter password?

There have been quite a few cases of yahoo no longer staying signed in if one closes the browser for a moment, not only in default browsers , but in the several excellent others as well. This specific simple fix is for the rest of us "late in life learners".
If you open email from bookmark/ favorites, just sign in (again to your email), now save this page to same place as original: overwrite/replace with new one.
It is often that the http address is not for the signed in period or it gets changed.
In Maxthon, after signing in to yahoo, for example, shorten the http address at top to end with neo/launch? by deleting everything after it. Copy and paste into Maxthon setup as home page or just as bookmark if you wish.

Here's what I now have in M as my home page: https://login.yahoo.com/config/login...o.com/%3f_bc=1. This will automatically open the sign in page for my.yahoo, with my PW and username in the proper fields. All I have to do is click enter and the desired home page shows and the url now is: http://my.yahoo.com/?_bc=1. Not sure where to add "neo/launch?"......

I am not sure that your cookie managers are keeping the 2 week yahoo sign in cookie. I also like these tools yet have to double check that none , including Maxthon, are set to delete cookies upon closing. Finding or settling on only one cookie manager is the standard wisdom. That said, this is now the http that keeps me signed in after unchecking"deletebrowser history" in Maxthon (tools/internet options if delete browser). I am using M 2.5.16 and fully acknowledge that some temp. files can pile up and are considered a privacy risk.
http://us.mg4.mail.yahoo.com/dc/launch?

You say this started after playing around with cookie eaters? Have you excluded the Yahoo cookies from being eaten? In CCleaner, click on Options, then Cookies,click on the cookie name, then the right arrow to move it to exclusions. The Maxthon cookie eater may have the same options, I am unfamiliar with it. A Guy

First, thanks for all your suggestions and help. I was finally able to get my.yahoo to automatically come up in both computers without having to inset my username and pw. Amd i have settled on CCleaner to manage the cookies, and a few other things. As to how I actually solved the problem, I don't know! I figured that I would simultaneously look at all relevant settings between both computers. with special attention to allowed cookie, hoping that I could let you know how I did it. Well, this turned out to be a very confusing task and unfortunately I can't come up with a satisfying answer. There are some similar and some different cookies bwtween the two computers, and yet both now bring up my.yahoo. I tried to figure it out, but couldnt. But at least things are working as I want them to...