You cannot submit an application for St Kitts and Nevis citizenship yourself, only through an approved agent, and that agent will conduct their initial background checks on you.
Your application might be refused if you do not comply with one or several requirements of the citizenship by investment program. If that is the case, immigration lawyers will be able to offer you a solution or an alternative scheme in a different jurisdiction where you would fit the criteria.
Another reason is a failure on your part to provide full details about yourself or provide them truthfully which will be revealed during due diligence checks.
However, in case of a refusal, you will only lose the due diligence fee as the investment is done strictly after an approval in principal.