Is it permissible to observe i'tikaaf at any time other than the last ten days of Ramadaan?.
Yes, it is permissible to observe i'tikaaf at any time, but the best is to do so during the last ten days of Ramadaan, following the example of the Messenger of Allaah (peace and blessings of Allaah be upon him) and his companions (may Allaah be pleased with them). It was narrated that the Prophet (peace and blessings of Allaah be upon him) also observed i'tikaaf during Shawwaal in some years.
And Allaah is the Source of strength. May Allaah send blessings and peace upon our Prophet Muhammad and upon his family and companions.