Undecrypt using the OpenSSL EVP API?
You should packetize, or recordize, the messages into discrete units of a size reasonable for your protocol. Each record should be independently encrypted with its own IV. As an example, look at TLS 1.2 record or IPsec ESP packets. If a record is corrupted it can be discarded without impacting other records.

EDIT:

As pointed out by @poncho, TLS incorporates an implicit sequence number in the MAC calculation. Thus this may not be a good example. He also points that DTLS includes an explicit sequence number, and thus may be a better example.