By striking to support Syria, they would essentially prove the US point that Iran is dangerous and open the door to, at a minimum, an Israeli air strike on their facilities.
Moreover, based on recent activity, I think Hezbollah realizes that it put itself into a terrible position and wants to keep Israel neutral - their fighters have no supply lines right now for rearming and are feeling vulnerable in their own country.
Ultimately, the strike will probably just neutralize recent Assad advances and ensure the war grinds on.
ἡ δὲ κἀκ τριῶν τρυπημάτων ἐργαζομένη ἐνεκάλει τῇ φύσει, δυσφορουμένη, ὅτι δὴ μὴ καὶ τοὺς τιτθοὺς αὐτῇ εὐρύτερον ἢ νῦν εἰσι τρυπώη, ὅπως καὶ ἄλλην ἐνταῦθα μίξιν ἐπιτεχνᾶσθαι δυνατὴ εἴη. – Procopius
Ummaka qinnassa nīk!
*MySmiley*