Can there be an example, where a force acts continuously but work is not done?

Yes. there is a possible case, when the force is perp. to disp. as in that case the dot product of theirs, i.e. work gives zero as result. For eg. Uniform circular motion.

Work can be zero even when there is a force. The centripetal force in a uniform circular motion, for example, does zero work because the kinetic energy of the moving object doesn't change. Likewise when a book sits on a table, the table does no work on the book despite exerting a force equivalent to mg upwards, because no energy is transferred into or out of the book. The work done by a force acting on an object depends on the inertial frame of reference, because the distance covered while applying the force does. Due to Newton's law of reciprocal actions there is a reaction force; it does work depending on the inertial frame of reference in an opposite way. The total work done is independent of the inertial frame of reference.