What is the explanation for the כי- suffix on the words חַיָּיְכִי and הַמְעַטְּרֵכִי in Psa. 103:4?
The כִי- (-kî) 2nd fem sg suffix (which appears also in vv. 3 and 5) is explained as simply a rare (or possibly Aramaizing) form of the suffix: see Gesenius Kautzsch Cowley, §58g (for the verb) and §91e for the noun. Basically the same explanation is given in Joüon-Muraoka, at §61i (verb), and §94i (noun). See also p. 269 of Geoffrey Khan's discussion of pronominal suffixes from the Encyclopedia of Hebrew Language and Linguistics, ed G. Khan et al. (Brill, 2013), Vol. 3, pp.267-272.
It is a feminine suffix because the psalmist is "speaking to" his nephesh, "soul" ("Bless the LORD, O my soul...", 103:1-2), and "soul" is grammatically feminine, and the antecedent of all these 2nd fem sg pronouns in vv. 3-5.