Air Carrier First Officer describes his inability to contact his Dispatcher via ACARS and relates a previous similar occurrence. The Dispatcher advises that he never received the messages.

Narrative

We where assigned holding while inbound to LGA on the KORRY arrival. NFP sent a ACARS message from the enroute delay page stating 'holding' with all the pertinent information and requesting a bingo number and alt weather. After approx ten minutes no response; I sent a second message this time using the misc report message function. No responses came from Dispatch. Since; our workload increased as we changed from one hold to another and ATC changed the EFC time the Captain had a bingo fuel number planned which we agreed upon so we continued inbound to LGA. If the hold would have continued ten minutes more a radio call was the next option. Upon landing at LGA the Captain called Dispatch to query and they advised that they missed the messages and no alerts came through. This is the second time in two weeks that I've personally ACARS'ed in-flight messages to Dispatch and received no response. The past week was a gate related station not answering the radio message. The Dispatcher in that case said; 'I didn't see your messages it went to a different Dispatcher...this thing is messed up'....