"I don't know based on the rulebook."

The rulebook context provided does not explicitly state what happens if a player cannot pay the egg cost required to explore a cave multiple times in one round. It does explain the costs for exploring a cave multiple times (e.g., 1 coin for the first time, 1 coin and 1 egg for the second time, and 1 coin and 2 eggs for the third time) and specifies that eggs can be paid from dragons or nests on the player mat (Page 10). However, it does not clarify whether the player is prevented from exploring if they cannot pay the required cost or if there is an alternative resolution.

To answer this question definitively, the rulebook would need to include a rule addressing situations where a player cannot pay the required cost for an action.

Source: Wyrmspan Rulebook (pp. 10, 11, 5, 8)