How do I rewrite the following sentence so it is more formal, using a phrasal verb in place of the part in bold?
Despite mounting evidence, they continue to stick to their belief.
One problem with the example sentence is that continue to is redundant with stick to, which already means “to persist; to continue.” Redundancy will exacerbate any informality in the sentence.
Regarding phrasal verbs – they are not always informal, but as Wikipedia notes:
Thus, a simple way to raise the register is to replace Anglo-Saxon verbs like stick with a Latinate verb meaning exactly the same thing:
However, there's an even better choice when it comes to beliefs:
The word maintain means both to keep something up and to affirm a belief, so in a situation like this, both senses contribute to the meaning.