The word botaban is the imperfect form of botar in the third person plural.
See the full botar conjugation

botar

Cada vez que botaban una nave grande, invitaban a algún dignatario de Londres al tren para dar un discurso, romper una botella de champán, lanzarlo por la grada en el río y hacia el mar.
So whenever they'd launch a big ship, they would invite some dignitary up from London on the train to make a speech, break a bottle of champagne over the bows, launch it down the slipway into the river and out to sea.
Lo botaban de un trabajo tras otro.
He was getting bounced from one job after another.
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