what causes tectonic plates to stop moving temporarily?

Answer 1

If they get hung up on other tectonic plates they'll stop (or slow, at least), pressure will build up, and finally it'll release all at once in an earthquake.

Answer 2

Basically, if they run into other tectonic plates you get problems. That was actually what happenned with Pangea--all the plates ran into each other, stopping plate movement. This slowed down sea floor spreading and caused deep sea subsidence, dropping the oceal level hundreds of meters. This, along with other environmental changes, led to the Permian Extinction- the biggest extinction in earth history.