We deal with the Sales Manager but suspect the CEO is behind these problems. Replacing this supplier is impossible because they have a unique product our clients demand. How to communicate our dissatisfaction and need for urgency without fracturing or hurting the relationship? FYI they're in a developing country that differs from typical Western standards and behaviors.
This is a very typical challenge while doing business in the multicultural contexts, specially if you have business relations in developing part of the world. Few suggestions:
1. Try to have couple of physical meetings which always bring crucial changes in the business relationship.
2. Emphasize more on having personal relationship over business which might solve half the issue if it is not a personality traits of the CEO.
3. Try to build relationship with the stuff of the company who are responsible for the operations. Build the relationship by giving 'not very expensive' souvenir gifts as token of appreciation for their continued support.
4.For long term sustainability of the business, you must look for other options. If need be, put some effort to develop alternative supplier.
Feel free to ask if you need further clarification. Wish you all the best :)