Off hand, it sounds like you've got something that is clearing your cookies periodically. New anti-virus software? Done something exotic with your browser cookie retention rules?
There is an ad (for ETrade, I think) that will hug the bottom of the page. But, if you allow cookies, you should only see it once a day.
Logging off unexpectedly is almost always the result of IH not being able to read your cookies.
I don't know what the "small square requester" is, but it may be what is causing your cookie issue. Figure out where that's coming from and your other problems may vanish.
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