In Catholic evening prayer, why do some days have Psalm prayers, other days do not? Nov 9, feast of St. John Lateran, feast, evening prayer, no psalm prayer. 
Nov 10, St Leo, pope and Doctor, memorial,, evening prayer, psalm prayer. 
Nov 11, St Martin of tours, bishop, memorial, evening prayer, no psalm prayer

Why some days are there psalm prayers, other days not?
The psalm prayer consists of optional prayers that may be said after each psalm. The General Instruction of the Liturgy of the Hours describes them as follows:


  112. Psalm-prayers for each psalm are given in the supplement to the Liturgy of the Hours, to help in understanding them in a predominantly Christian way. They may  be used in the ancient traditional way: after the psalm a period of silence is observed, then the prayer gathers up and rounds off the thoughts and inspirations of those taking part (Source: http://dariasockey.blogspot.it/2013/04/divine-office-factoid-5-perenniel-psalm.html).


They appear in the Office of Readings, Morning Prayer (Lauds), the Daytime Prayers (Terce, Sext, and None), and Evening Prayer (Vespers). They do not appear at Night Prayer (Compline).

There are a number of reasons why a psalm prayer might not appear after the recitation of a given canticle. First of all, a psalm prayer appears only after a true psalm, one of the 150 chapters of the Book of Psalms (as numbered in the Vulgate, not in the Hebrew Old Testament). Hence, they never appear after the second canticle of Lauds (which is always taken from an Old-Testament source other than the Psalms) or the third canticle of Vespers (which is always taken from the New Testament).

Second, especially in the Office of Readings and the Daytime Prayers, sometimes a psalm runs continuously, constituting two or three of the canticles. (Also Psalm 118, or 119 in the Hebrew, is so long that it is spaced out during several weeks.) In those cases, the psalm prayer is found only at the end of the complete psalm.

Since the psalm prayer is optional and not usually used in public recitation, many editions omit it altogether.

(However, the online edition on iBreviery in English, which uses the American text, does have them.)