Though a Succah needs only proper walls and a schach roof to enable one to fulfil the mitzvah of Succah, when possible the Succah should be decorated as well. (Mishna Berurah OC 638 section 11in the name of Elya Raba) Decorations used for the Succah may not be used for other purposes or even removed from the Succah during the eight (nine-in the diaspora) days of Sukkot.
The rational behind the prohibition to use or remove Succah decorations is taught in Gemarah Shabat 22a. Since the decorations were set aside for the purpose of a mitzvah, it is a disgrace to the mitzvah if the item is used for other purposes.
It is clear that items used for decorations may not be removed for personal purposes. What about removing decorations to preserve them from damage? Can one remove the Decorations so they not get wet in rain?
The Gemarah Beitzah 30b brings the Tanaic source that prohibits the use of decorations during Sukkot. The Briyta also teaches that if a person were to make a stipulation allowing him the use of the items being used as decorations, in some other way, he may act in accordance with his stipulated condition. This condition should ideally be made while putting up the decorations but can be made at any point until sunset of the day proceeding Sukkot.
Using such a condition, one may stipulate that he allows himself the right to remove some or all the decorations at any time in case of rain or any other potential damage. There are even more lenient opinions. Based on the opinion of the Taz, that no one puts up decorations to be stolen or damaged we can assume the decorations were put up on condition they are well preserved. Therefore any time the decorations may be exposed to damage we assume an implicit stipulation allowing their removal for the purpose of preservation. Ideally one should make an explicit stipulation but may remove the decorations in case of rain even based on the implicit stipulation.
The explicit or implicit stipulation allows the removal of decorations at any time even on Yom Tov and Shabat. Yet one must be careful not to transgress other prohibitions of Shabat and Yom Tov. For example some authorities point out that decorations should be tied with a bow and not a regular double knot to avoid the problem of unknotting a knot on Shabat or Yom Tov.