[romnon]

Umm, proceed and persist sounds better imo.

[chrismorgan]

Or “pursue and persist”.

“Cease and desist” has nice assonance, I feel “pursue and persist” matches a little more in that regard, though both are decent.

As regards meaning, “proceed” and “pursue” are both good, taking slightly different angles but to essentially the same purpose.

[xanderlewis]

Maybe, but ‘continue’ is a better negation of ‘cease’. Proceed can mean (usually means?) to do something one has not yet started, rather than to not cease.

[asveikau]

By the latin roots:

Continue - hold together (cum + tenere -- same root as contain)

Proceed - go forward (pro + cedere)

[xanderlewis]

I'm not sure what you're trying to conclude...