On line 159 of account/index.php you have:
<?php $_SESSION['product_case'."".$row_rs_favorite["title"] ." ".$row_rs_favorite["subtitle"] .""] = $row_rs_favorite['case'] ?>
This causes some session variable names to have special characters which aren't allowed. I think the specific issue is the "!" in one of them, but they also have slashes, commas, and single quotes, but I think the exclamation point is the one causing issues.
I commented out that line and the user stays logged in.