。。
Keep your promises. Otherwise your reputation will suffer.
Literal
Promise [topic-は] keep-[command-なさい]. So-do-if-not reputation [obj-を] drop-[polite-ます][assertion-よ].
Two-clause warning. そうしないと ('if you don't do so') is a common bridging phrase setting up the consequence of not following the preceding instruction. 評判を落とす ('drop one's reputation') is a set collocation — 落とす ('drop') is the transitive verb for actively causing something to fall, here metaphorically applied to reputation.