1- Islam, at the beginning (of i'tikaf) and throughout.
The i'tikaf of a kafir is not valid because i'tikaf is a branche of faith.
If one reverts from Islam while in i'tikaf, his i'tikaf is nullified.
2- Sanity/discrimination. However, puberty is not stipulated.
Hence, the i'tikaf of a young boy is valid, unlike that of the insane because he is not qualified for worship just like a kafir.
3- Purity from major hadath, be it menstruation, postnatal bleeding, or janaba because staying in a mosque while in a menstrual or postnatal period, or in a state of janaba is sinful.
If menstruation, postnatal bleeding, or janaba occurs during i'tikaf, the
person should leave the mosque immediately.