Same in unity 5.5.1.
Size of the scrollbar change automatically when press Play! (Size persistant: 0.43824)

It is caused by the scrollrect's attempt to scale the scrollbar in order to represent the portion of the content area that you are currently viewing (like a standard windows scrollbar does).
In order to circumvent this behaviour you can remove the scrollbar reference from the scrollrect and add a small script which reads the ScrollBar.value and then sets the ScrollRect.normalizedPosition accordingly instead.

http://docs.unity3d.com/462/Documentation/ScriptReference/UI.Scrollbar-value.html
http://docs.unity3d.com/ScriptReference/UI.ScrollRect-normalizedPosition.html

i found a solution to this problem, i bet you can use as well, this is the link of the solution/solved problem: http://forum.unity3d.com/threads/anybody-got-scrollrects-to-cooperate-with-dynamic-content.265600/

they said that you need to use a component called "Content Size Fitter", and set the axis that u want to fit within the elements and the RectTransform object of the content of the scrollview. it worked for me and saved me :) if u are getting resizing errors with scrollbars and scrollrects it worths to try in your project.

Im getting the same, exactly error/issue... i expect that someone could give us a light... to our problem...

Same thing here, and I can add that I have the same issue with the "Value" of the scroll bar.

If I put the value I want, another value is randomly set. Also, after a play, sometimes the value isn't reset to the original value.