As mentioned in this Meta question, approval of an edit suggestion gives the suggester +2 reputation.
If the suggestion is rejected, does it cost the suggester any rep?
No, but repeated edit suggestion rejections from multiple users will cause your edit suggestion rights to be suspended for (n) days, where n is currently 7.
Note that after a recent change, automatic rejections due to edit conflicts are ignored and won't affect the suggested edit ban mechanism. (only rejections made by actual users)