The primary assumption is that a prospect is an amateur. This assumption is translated into initial eligibility. Thus, eligibility is something that can be lost. NCAA Rule 12.1.1 begins by stating that "An individual loses amateur status..."
There exists basically one criteria for the loss of amateur status - having received value for competing.
This is of particular importance to athletes in individual sports and international students. Throughout out the world is it not uncommon for a high school athlete in such sports as tennis and ice-skating to achieve such a level of skill as to be able to compete for value, primarily cash. In many countries, younger athletes can earn sports on professional teams, such as soccer and hockey. Such "professional" competition costs an athlete amateur status and renders them ineligible for NCAA competition.
Promise or actual payment of money deferred until after college will affect the loss of amateur status. If play was done in consideration for cash or cash equivalents regardless of when that value is actually paid out, then the athlete loses amateur status.
Reimbursement of expenses is not "pay" and is permissible. But there are many limitations that are very narrow and are clearly set out in the NCAA regulations.
Beyond "play for pay", other activities can cause loss of amateur status. These include use of agents, employment or promotional activities based on athletic fame or prowess, receipt of donations, and being in a professional draft.