Many Shules place the Torah's crown on the Sefer Torah only by Shabbos/Yom Tov Shachris, why is that so?
Edit: I added Yom Tov as I agree with msh210's observation that it is also true on Yom Tov.
As Double AA said, it might just be the time when the donor's there. My guess, however, would be for Kavod Shabbos. If you had the crown on all the time, it wouldn't be special when you saw it on Shabbos.
But that leads to the question of why not put it on during Shabbos Minchah? I'd guess that this is because at Shabbos Minchah time, the Kedushah of Shabbos starts to fade away. This is why we often say the Tzikasichah prayer towards the end of Minchah, to try and retain the Kedushah of Shabbos.
In many shuls, this is nothing more than a space constraint, esp. if the Shabbat davening is in a chapel during weekdays and a bigger shul on Shabbat. Usually, the chapel has a small ark, so there just isn't room to store it with the crown, esp. if the small ark has just enough space for 1 or 2 Sifrei Torah.
My shul is exactly like this. We pray in the smaller chapel all the time except Shabbat and Yom Tov. The big shul's ark is so large that they can store the Sifrei Torah with the crowns on them.
Another possible factor - the crown can add a lot of weight to an already heavy Torah. If elderly people are the regular "miyannaires" (I see this phenomena in a number of small-town shuls, esp. Conservative ones), many of them can't carry the Torah with that added weight. On Shabbat, these shuls attract more people and families, and often, younger stronger men can carry the Torah with its crown.