Grammatical explanation for the different use of ‘continue’ and ‘continues’

The explanation, I'm afraid, is that may and hope are different words, and have different syntactic requirements.

There is some generality here: may is a modal auxiliary, like can, should, will, and these are always followed by the base form of the verb.

But it is not predictable from its meaning that hope takes as its object a tensed clause, optionally introduced by that. (It can also take a non-finite to clause). This is part of the "dictionary entry" for hope, and needs to be learnt along with its spelling and pronunciation. Expect (with similar though not identical meaning) takes the same kinds of object, but anticipate (again similar in meaning) can also take an -ing clause, but not a to clause).

Your love continues to grow. (usual S with singular third person) I hope doesn't affect the verb continues. I hope, the love continues, two different subjects with each their verb.

Your love may continue to grow. This is the same structure as:

• "your love will continue"
• "your love should continue"
• "your love can continue"
• "your love might continue"

May, should, could, will, might and others are modal verbs, they eat up the S rule for the third person.