One should never think that he is unworthy of davening. Even if one feels that he quickly loses the sanctity he feels while he is davening, that should not cause him to lose hope.
Sefer Chemda Genuza (Chelek 2, page 195) quotes Rav Yehoshua of Tomashov zy"a as saying in the name of his father, Rav Yosele of Tomashov zy"a (a student of the Chozeh of Lublin zy"a) that one should never say: In my entire life, I have never davened properly. I have never done a single mitzvah properly. Even when I do manage a bit of avodah, I lose the inspiration soon thereafter. Why should I even try?
One should never even think this because such thoughts could lead him to lose everything. Rather, one should say that the past is over and done with, and from now on, I commit to improve and do everything I can to daven and serve Hashem properly.
The proof of this is from the sun. Starting from the morning, it gets higher and stronger until midday. It then begins to get lower and weaker, until it disappears from the horizon completely. Still and all, it gets up again the next day and shines again. It doesn't say: Why should I even try? Even if I reach the heights, I will end up falling. Rather, it does its part and doesn't worry about what was in the past. That is how one's avodah should be.
This is the meaning of the pasuk in Tehillim (113:30): "From the rising of the sun until its setting, the name of Hashem is praised." We see how the sun rises every day, only to set afterwards, and it never gives up. So too, we should praise Hashem every day and not worry about our setbacks of the past.
