Throughout history, some cryptographic systems were broken by finding patterns in encrypted messages (like frequent chars in a particular language), and thereby discovering the cipher. These classic systems, which relied on algorithms unknown to the attacker, were broken by analyzing the messages and detecting patterns. This allowed attackers to induce the algorithm that was used.
The security of modern cryptography is based on a large key and applying non-reversible mathematics to a message to obtain an encrypted message. In these modern systems it is impossible to apply reverse engineering to a message because it requires more computational capacity than available.
Since there is currently a lot of storage capacity to store an giant amount of encrypted messages, knowing that it was generated with the same key and the same algorithm, it is not possible to analyze them, for instance by finding repetitive patterns, to be able to deduce the key?