If you can't come, please contact us as soon as possible.
Literal
Come-can-not case [topic-は], as-much-as-possible early contact-do-please.
~場合 ('case / occasion / circumstance') functions as a conditional frame — '場合は' = 'in the case that / if.' 来れない is the colloquial shortened potential negative of 来る (properly 来られない); this 'ら-less' form is widespread in speech and informal writing. できるだけ ('as much as possible') is a fixed adverbial.