There is a rabbinic rule that the shofar is not blown on Shabbat. From what I can find, this is based solely on the Talmudic passage Rosh Hashanah 29b. The concern is that using the shofar on Shabbat would involve carrying it a long enough distance to be considered work.
Many Messianic Jewish congregations use the shofar regularly. There are scriptural reasons to do so: God's people are assembling, and announcing the imminent arrival of their Lord.
Does anyone have more information about why Rabbinic Jews do not use the shofar more regularly?